Econ 210 Exam 4 5
In a regression analysis, the variable that is being predicted
The dependent variable
Refer to Exhibit 12-3. Based on the above estimated regression equation, if advertising is $3,000, then the point estimate for sales (in dollars) is
$66,000
Least squares criterion
(Yi-Yhat)^2
Pooled estimator of p
An estimator of a population proportion obtained by computing a weighted average of the sample proportions obtained from two independent samples
If the coefficient of determination is a positive value, then the coefficient of correlation must be
Either negative or positive
To construct an interval estimate for the difference between the means of two populations when the standard deviations of the two populations are unknown, we must use a t distribution with (let n1 be the size of sample 1 and n2 the size of sample 2)
(n1 + n2 − 2) degrees of freedom
The number of degrees of freed for the appropriate chi-square distribution in a test of independence is
(number of rows minus 1)*(number of columns minus 1)
In the case of the test of independence, the number of degrees of freedom for the appropriate chi-square distribution is computed as
(r - 1)(c - 1)
As a general guideline, the research hypothesis should be stated as the
Alternative hypothesis
Refer to Exhibit 12-1. The coefficient of determination equals
+1
Refer to Exhibit 12-5. The coefficient of determination equals
+1
Refer to Exhibit 11-3. The point estimate for the difference between the proportions is
-0.02
Refer to Exhibit 11-1. The 95% confidence interval estimate for the difference between the populations favoring the products is
-0.024 to 0.064
Refer to Exhibit 11-3. The 95% confidence interval for the difference between the two proportions is
-0.068 to 0.028
Refer to Exhibit 12-6. The sample correlation coefficient equals
-0.4364
Refer to Exhibit 12-2. The least squares estimate of b1 equals
-0.7647
Refer to Exhibit 12-2. The sample correlation coefficient equals
-0.99705
Refer to Exhibit 12-5. The least squares estimate of b1 (slope) equals
-1
Refer to Exhibit 12-5. The sample correlation coefficient equals
-1
Refer to Exhibit 12-6. The least squares estimate of b1 equals
-1
Refer to Exhibit 12-5. The point estimate of y when x = 10 is
-4
The test for goodness of fit
. is always a one-tail test with the rejection region occurring in the upper tail
Refer to Exhibit 11-1. The point estimate for the difference between the two population proportions in favor of this product is
0.02
Refer to Exhibit 11-1. The standard error of p bar 1 - p bar 2 is
0.0225
Refer to Exhibit 11-3. The standard error of p bar 1 - p bar 2 is
0.0243
Refer to Exhibit 11-1. At 95% confidence, the margin of error is
0.044
Refer to Exhibit 12-6. The coefficient of determination equals
0.1905
In a regression analysis if SSE = 500 and SSR = 300, then the coefficient of determination is
0.3750
If a data set has SST = 2,000 and SSE = 800, then the coefficient of determination is
0.6
In a regression analysis if SSE = 200 and SSR = 300, then the coefficient of determination is
0.6000
Refer to Exhibit 12-4. The coefficient of determination is
0.625
In a regression analysis if SST = 4500 and SSE = 1575, then the coefficient of determination is
0.65
Refer to Exhibit 12-4. The coefficient of correlation is
0.7906
Refer to Exhibit 12-2. The coefficient of determination equals
0.9941
If all the points of a scatter diagram lie on the least squares regression line, then the coefficient of determination for these variables based on this data is
1
Refer to Exhibit 12-4. The least squares estimate of the slope is
1
Refer to Exhibit 11-5. The calculated value for the test statistic equals
1.6615
The degrees of freedom of a contingency table with 6 rows and 3 columns is
10
Refer to Exhibit 11-7. The expected frequency for the Business College is
105
Refer to Exhibit 12-6. The least squares estimate of b0 equals
11
The degrees of freedom for a contingency table with 12 rows and 12 columns is
121
Refer to Exhibit 11-8. The expected number of adults who prefer coffee is
150
Refer to Exhibit 12-2. The least squares estimate of b0 equals
16.41176
Refer to Exhibit 11-4. The number of degrees of freedom associated with this problem is
2
Refer to Exhibit 12-4. The MSE is
2
Refer to Exhibit 12-4. The least squares estimate of the Y intercept is
2
Refer to Exhibit 12-3. Using a = 0.05, the critical t value for testing the significance of the slope is
2.131
Refer to Exhibit 11-4. The calculated value for the test statistic equals
4
Refer to Exhibit 11-7. The calculated value for the test statistic equals
4.29
Refer to Exhibit 12-3. The critical F value at a = 0.05 is
4.54
Refer to Exhibit 12-3. The F statistic computed from the above data is
45
Refer to Exhibit 11-7. The hypothesis is to be tested at the 5% level of significance. The critical value from the table equals
5.991
Refer to Exhibit 11-4. The expected frequency for each group is
50
Refer to Exhibit 12-5. The least squares estimate of b0 (intercept)equals
6
Refer to Exhibit 12-3. The t statistic for testing the significance of the slope is
6.709
Refer to Exhibit 11-5. The expected frequency of seniors is
60
Refer to Exhibit 11-8. The test statistic for this test of independence is
62.5
Refer to Exhibit 11-8. With a .05 level of significance, the critical value for the test is
7.815
Regression analysis was applied between sales (in $1,000) and advertising (in $100), and the following regression function was obtained. y^ = 80 + 6.2x Based on the above estimated regression line, if advertising is $10,000, then the point estimate for sales (in dollars) is
700,000
Refer to Exhibit 11-5. The expected number of freshmen is
90
The degrees of freedom for a contingency table with 10 rows and 11 columns is
90
Regression analysis was applied between sales (in $1000) and advertising (in $100) and the following regression function was obtained. y^ = 500 + 4x Based on the above estimated regression line if advertising is $10,000, then the point estimate for sales (in dollars) is
900,000
should not be rejected
A two-tailed test is performed at 95% confidence. The p-value is determined to be 0.09. The null hypothesis
In regression analysis, which of the following is not a required assumption about the error term e?
All are required assumptions about the error term.
In order not to violate the requirements necessary to use the chi-square distribution, each expected frequency in a goodness of fit test must be
At least 5
As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution
Becomes smaller
In regression analysis if the dependent variable is measured in dollars, the independent variable
Can be in any units
The sampling distribution for a goodness of fit test is the
Chi-square distribution
In conducting a hypothesis test about p1 - p2, any of the following approaches can be used except
Comparing the observed frequencies to the expected frequencies
The interval estimate of the mean value of y for a given value of x is the
Confidence Interval
A measure of the strength of the relationship between two variables is the
Correlation
pu - po = 0
Exhibit 10-11 An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below. Under Age of 18 n1 = 500 Number of accidents = 180 Over Age of 18 n2 = 600 Number of accidents = 150 We are interested in determining if the accident proportions differ between the two age groups. Refer to Exhibit 10-11 and let pu represent the proportion under and po the proportion over the age of 18. The null hypothesis is
μ1 -μ2 = 0
Exhibit 10-13 In order to determine whether or not there is a significant difference between the hourly wages of two companies, the following data have been accumulated. Company 1 n1 = 80 MeanX1 = $10.80 Omega1= $2.00 Company 2 n2 = 60 MeanX1 = $10.00 Omega1=$1.50 Refer to Exhibit 10-13. The null hypothesis for this test is
3
Exhibit 10-4 The following information was obtained from independent random samples. Assume normally distributed populations with equal variances. Refer to Exhibit 10-4. The point estimate for the difference between the means of the two populations is
should not be rejected
Exhibit 10-5 The following information was obtained from matched samples. Refer to Exhibit 10-5. If the null hypothesis is tested at the 5% level, the null hypothesis
0.50
Exhibit 10-8 In order to determine whether or not there is a significant difference between the hourly wages of two companies, the following data have been accumulated. Company A: Sample size 80 Sample mean $16.75 Population standard deviation $1.00 Company B: Sample size 60 Sample mean $16.25 Population standard deviation $0.95 Refer to Exhibit 10-8. A point estimate for the difference between the two sample means is
2.0
Exhibit 10-9 Two major automobile manufacturers have produced compact cars with the same size engines. We are interested in determining whether or not there is a significant difference in the MPG (miles per gallon) of the two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data show the results of the test. Refer to Exhibit 10-9. The mean for the differences is
2.256
Exhibit 10-9 Two major automobile manufacturers have produced compact cars with the same size engines. We are interested in determining whether or not there is a significant difference in the MPG (miles per gallon) of the two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data show the results of the test. Refer to Exhibit 10-9. The test statistic is
2.25
Exhibit 11-2 We are interested in determining whether or not the variances of the sales at two music stores (A and B) are equal. A sample of 26 days of sales at store A has a sample standard deviation of 30 while a sample of 16 days of sales from store B has a sample standard deviation of 20. Refer to Exhibit 11-2. The test statistic is
should not be rejected
Exhibit 11-3 The contents of a sample of 26 cans of apple juice showed a standard deviation of 0.06 ounces. We are interested in testing to determine whether the variance of the population is significantly more than 0.003. Refer to Exhibit 11-3. At 95% confidence, the null hypothesis
σ2 ≤ 0.003
Exhibit 11-3 The contents of a sample of 26 cans of apple juice showed a standard deviation of 0.06 ounces. We are interested in testing to determine whether the variance of the population is significantly more than 0.003. Refer to Exhibit 11-3. The null hypothesis is
greater than 0.10
Exhibit 11-3 The contents of a sample of 26 cans of apple juice showed a standard deviation of 0.06 ounces. We are interested in testing to determine whether the variance of the population is significantly more than 0.003. Refer to Exhibit 11-3. The p-value for this test is
12.68
Exhibit 11-5 n = 14 s = 20 H0: σ2 ≤ 500 Ha: σ2 > 500 Refer to Exhibit 11-5. The test statistic for this problem equals
should be rejected
Exhibit 11-6 We want to test the hypothesis that the population variances are equal. Refer to Exhibit 11-6. At 95% confidence, the null hypothesis
2.4
Exhibit 11-6 We want to test the hypothesis that the population variances are equal. Refer to Exhibit 11-6. The test statistic for this problem equals
0.10
Exhibit 11-7 We want to test the hypothesis that population A has a larger variance than population B. Refer to Exhibit 11-7. The p-value is approximately
500
Exhibit 13-1 SSTR = 6,750 H0: μ1=μ2=μ3=μ4 SSE = 8,000 Ha: at least one mean is different nT = 20 Refer to Exhibit 13-1. The mean square within treatments (MSE) equals
greater than 0.10
Exhibit 13-2 Refer to Exhibit 13-2. The null hypothesis is to be tested at the 5% level of significance. The p-value is
should not be rejected
Exhibit 13-3 To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the 3 treatments. You are given the results below. Refer to Exhibit 13-3. The null hypothesis
50.00
Exhibit 13-4 In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five treatments (a total of 65 observations). The following information is provided. SSTR = 200 (Sum Square Between Treatments) SST = 800 (Total Sum Square) Refer to Exhibit 13-4. The mean square between treatments (MSTR) is
10
Exhibit 13-4 In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five treatments (a total of 65 observations). The following information is provided. SSTR = 200 (Sum Square Between Treatments) SST = 800 (Total Sum Square) Refer to Exhibit 13-4. The mean square within treatments (MSE) is
60
Exhibit 13-5 Part of an ANOVA table is shown below. Refer to Exhibit 13-5. The mean square between treatments (MSTR) is
4
Exhibit 13-5 Part of an ANOVA table is shown below. Refer to Exhibit 13-6. The number of degrees of freedom corresponding to between treatments is
are not equal
Exhibit 13-6 Part of an ANOVA table is shown below. Refer to Exhibit 13-6. The conclusion of the test is that the means
2.00
Exhibit 9-4 The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes with a standard deviation of 0.5 minutes. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes. Refer to Exhibit 9-4. The test statistic is
0.1056
Exhibit 9-5 A random sample of 100 people was taken. Eighty-five of the people in the sample favored Candidate A. We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 80%. Refer to Exhibit 9-5. The p-value is
If we are testing for the equality of 3 population means, we should use the
F Statistic
1.53
For a one-tailed test (upper tail) at 93.7% confidence, Z =
1.328
For a two-tailed test, a sample of 20 at 80% confidence, t =
A statistical test conducted to determine whether to reject or not reject a hypothesized probability distribution for a population is known as a
Goodness of fit
will decrease
If the level of significance of a hypothesis test is raised from .01 to .05, the probability of a Type II error
37.3
In a completely randomized design involving four treatments, the following information is provided. The overall mean (the grand mean) for all treatments is
40
In an analysis of variance problem if SST = 120 and SSTR = 80, then SSE is
different levels of a factor
In the ANOVA, treatment refers to
the independent variable
In the analysis of variance procedure (ANOVA), "factor" refers to
If the cost of a Type I error is high, a smaller value should be chosen for the
Level of significance
The test statistic F is the ratio
MSR/MSE
An important application of the chi-square distribution is
Making inferences about a single population variance; testing for goodness of fit; testing for the independence of two variables
A population where each element of the population is assigned to one and only one of several classes or categories is a
Multinomial population
In a simple regression analysis (where Y is a dependent and X an independent variable), if the Y intercept is positive, then
None of these alternatives is correct.
There is a statistically significant difference in the average final examination scores between the two classes.
Refer to Exhibit 10-3. What is the conclusion that can be reached about the difference in the average final examination scores between the two classes? (Use a .05 level of significance.) Exhibit 10-3 A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information.
The difference between the observed value of the dependent variable and the value predicted by using the estimated regression equation is the
Residual
In analysis of variance, the dependent variable is called the
Response variable
In a regression analysis if r2 = 1, then
SSE must be equal to zero
The multiple coefficient of determination is
SSR/SST
Which of the following is correct?
SST = SSR + SSE
The degrees of freedom associated with a t distribution are a function of the
Sample size
More evidence against H0 is indicated by
Smaller p values
What is a statistical inference?
Takes the information from a sample to make a statement about the population
H0: μ ≤ 21.80 Ha: μ > 21.80
The average hourly wage of computer programmers with 2 years of experience has been $21.80. Because of high demand for computer programmers, it is believed there has been a significant increase in the average wage of computer programmers. To test whether or not there has been an increase, the correct hypotheses to be tested are
2.45
The critical value of F at 95% confidence when there is a sample size of 21 for the sample with the smaller variance, and there is a sample size of 9 for the sample with the larger sample variance is
Prediction interval
The interval estimate of an individual value of y for a given value of x
rejecting a true null hypothesis
The level of significance in hypothesis testing is the probability of
between 0.025 to 0.05
The producer of a certain bottling equipment claims that the variance of all their filled bottles is 0.027 or less. A sample of 30 bottles showed a standard deviation of 0.2. The p-value for the test is
standard deviation of the sampling distribution of (Mean x)1 - (Mean x)2
The standard error of (Mean x)1 - (Mean x)2 is the
Which of the following is a characteristic of a binomial experiment
The trials are independent
A goodness of fit test is always conducted as a
Upper-tail test
Which of the following descriptive statistics is not measured in the same units as the data
Variance
matched samples
When each data value in one sample is matched with a corresponding data value in another sample, the samples are known as
Refer to Exhibit 11-1. The conclusion of the test is that the Answers: a. distribution is uniform b. distribution is not uniform c. test is inconclusive d. None of these alternatives is correct.
a
Refer to Exhibit 11-1. The expected frequency for each group is Answers: a. 50 b. 1/3 c. 0.50 d. 0.333
a
Refer to Exhibit 11-6. At 95% confidence, the margin of error is Answers: a. 0.044 b. 0.064 c. 52 d. 0.0225
a
Refer to Exhibit 11-6. The point estimate for the difference between the two population proportions in favor of this product is Answers: a. 0.02 b. 100 c. 52 d. 0.44
a
The variable of interest in an ANOVA procedure is called
a factor
Scatter diagram
a graph of bi-variate data in which the independent variable is on the horizontal axis and the dependent variable is on the vertical axis
In a residual plot against x that does not suggest we should challenge the assumptions of our regression model, we would expect to see
a horizontal band of points centered near zero
Coefficient of determination
a measure of the goodness of fit of the estimated regression equation. It can be interpreted as the proportion of the variability in the dependent variable y that is explained by the estimated regression equation
Correlation coefficient
a measure of the strength of the linear relationship between two variables
Multinomial population
a population in which each element is assigned to one and only one of several categories. The multinomial distribution extends the binomial distribution form two to three or more outcomes
Least squares method
a procedure used to develop the estimated regression equation. The objective is to minimize
A variable that cannot be measured in terms of how much or how many but instead is assigned values to represent categories is called
a qualitative variable
Goodness of fit test
a statistical test conducted to determine whether to reject a hypothesized probability distribution for a population
Contingency table
a table used to summarize observed and expected frequencies for a test of independence
If we are interested in testing whether the mean of population 1 is significantly smaller than the mean of population 2, the
alt. hypothesis should say m1-m2<0
If we are interested in testing whether the proportion of items in population 1 is larger than the proportion of items in population 2, the
alternative hypothesis should state P1 - P2 > 0
The purpose of the hypothesis test for proportions of a multinomial population is to determine whether the actual proportions
are different than the hypothesized proportions
In order not to violate the requirements necessary to use the chi-square distribution, each expected frequency in a goodness of fit test must be
at least 5
Excel's ____ function is used to perform a test of independence. Answers: a. t-Test: Two Sample Assuming Equal Variances b. CHISQ.TEST c. NORM.S.DIST d. z-Test: Two Sample for Means
b
Refer to Exhibit 11-1. The hypothesis is to be tested at the 5% level of significance. The critical value from the table equals Answers: a. 7.81473 b. 5.99147 c. 7.37776 d. 9.34840
b
A multiple regression model has the form = 7 + 2 x1 + 9 x2 As x1 increases by 1 unit (holding x2 constant), is expected to
increase by 2 units
Refer to Exhibit 11-6. The standard error of p1-p2 is Answers: a. 100 b. 52 c. 0.0225 d. 0.044
c
In regression analysis if the dependent variable is measured in dollars, the independent variable
can be any units
If two independent large samples are taken from two populations, the sampling distribution of the difference between the two sample means
can be approximated by a normal distribution
Both the hypothesis test for proportions of a multinomial population and the test of independence employ the
chi squared
The sampling distribution for a goodness of fit test is the
chi-square distribution
In simple linear regression, r2 is the
coefficient of determination
The proportion of the variation in the dependent variable y that is explained by the estimated regression equation is measured by the
coefficient of determination
The interval estimate of the mean value of y for a given value of x is the
confidence interva
The interval estimate of the mean value of y for a given value of x is the
confidence interval
A measure of the strength of the relationship between two variables is the
correlation coefficient
If the coefficient of determination is a positive value, then the regression equation
could have either a positive or a negative slope
Refer to Exhibit 11-1. The calculated value for the test statistic equals Answers: a. -2 b. 20 c. 2 d. 4
d
The number of degrees of freedom for the appropriate chi-square distribution in a test of independence is Answers: a. k-1 b. n-1 c. a chi-square distribution is not used d. number of rows minus 1 times number of columns minus 1
d
In regression analysis, the response variable is the
dependent variable
Refer to Exhibit 11-4. The conclusion of the test (at 95% confidence) is that the
distribution is uniform
A variable that takes on the values of 0 or 1 and is used to incorporate the effect of qualitative variables in a regression model is called
dummy variable
A statistical test conducted to determine whether to reject or not reject a hypothesized probability distribution for a population is known as a
goodness of fit test
A statistical test conducted to determine whether to reject or not reject a hypothesized probability distribution for a population is known as a contingency test probability test goodness of fit test None of these alternatives is correct.
goodness of fit test
A statistical test conducted to determine whether to reject or not reject a hypothesized probability distribution for a population is known as a
goodness to fit test
Residual plot
graphical representation of the residuals that can be used to determine whether the assumptions made about the regression model appear to be valid
Refer to Exhibit 11-5. The p-value is
greater than 0.1
Refer to Exhibit 11-7. The p-value is
greater than 0.1
An example of statistical inference is
hypothesis testing
The test for goodness of fit
is always a one-tail test with the rejection region occurring in the upper tail
In a regression analysis, the variable that is being predicted
is the dependent variable
If a hypothesis is rejected at 95% confidence,
it must also be rejected at the 90% confidence
The mean square is the sum of squares divided by
its corresponding degrees of freedom
If a qualitative variable has k levels, the number of dummy variables required is
k − 1
Refer to Exhibit 11-4. The p-value is
larger than 0.1
Larger values of r2 imply that the observations are more closely grouped about the
least squares line
Refer to Exhibit 11-8. The p-value is
less than 0.005
When each data value in one sample is matched with a corresponding data value in another sample, the samples are known as
matched samples
A least squares regression line
may be used to predict a value of y if the corresponding x value is given
In regression analysis, the unbiased estimate of the variance is
mean square error
The least squares criterion is
min
A population where each element of the population is assigned to one and only one of several classes or categories is a
multinomial population
Refer to Exhibit 11-7. This problem is an example of a
multinomial population
When developing an interval estimate for the difference between two sample means, with sample sizes of n1 and n2,
n1 and n2 can be different sizes
Compared to the confidence interval estimate for a particular value of y (in a linear regression model), the interval estimate for an average value of y will be
narrower
The sampling distribution of is approximated by a
normal distribution
The sampling distribution of p bar 1 - p bar 2 is approximated by a
normal distribution
When conducting a good of fit test, the expected frequencies for the multinomial population are based on the
null hypothesis
Both the hypothesis test for proportions of a multinomial population and the test of independence focus on the difference between
observed frequencies and expected frequencies
Regression analysis is a statistical procedure for developing a mathematical equation that describes how
one dependent and one or more independent variables are related
In an analysis of variance, one estimate of σ2 is based upon the differences between the treatment means and the
overall sample mean
Refer to Exhibit 11-7. The conclusion of the test is that the
proportions have not changed significantly
Simple linear regression
regression analysis involving one independent variable and one dependent variable in which the relationship between the variables is approximated by a straight line
In regression analysis, an outlier is an observation whose
residual is much larger than the rest of the residual values
The required condition for using an ANOVA procedure on data from several populations is that the
sampled populations have equal variances
Refer to Exhibit 11-5. At 95% confidence, the null hypothesis
should not be rejected
The standard error of x1 and x2 is the
standard deviation of the sampling distribution of x1 and x2
The standard error of is the
standard deviation of the sampling distribution of xbar1-xbar2
Independent simple random samples are taken to test the difference between the means of two populations whose standard deviations are not known. The sample sizes are n1 = 25 and n2 = 35. The correct distribution to use is the
t distribution with 58 degrees of freedom
All of the following tests follow a chi-square distribution except
test for the difference between two means
All of the following tests follow a chi-square distribution except test of independence of two variables test for the difference between two proportions test for proportions of a multinomial population test for the difference between two means
test for the difference between two means
Residual analysis
the analysis of the residuals used to determine whether the assumptions made about the regression model appear to be valid. Residual analysis is also used to identify outliers and influential observations.
ANOVA table
the analysis of variance table used to summarize the computations associated with the F test for significance
ith residual
the difference between the observed value of the dependent variable and the value predicted using the estimated regression equation; for the ith observation the ith residual is yi-y^i
Regression model
the equation describing how y is related to x and an error term; in simple linear regression, the regression model is
Regression equation
the equation that describes how the mean or expected value of the dependent variable is related to the independent variable; in simple linear regression E(y) = Bo + B1x
Estimated regression equation
the estimate of the regression equation developed from sample data by using the least squares method. For simple linear regression, the estimated regression equation is
Confidence interval
the interval estimate of the mean value of y for a given value of x
Which of the following does not need to be known in order to compute the p-value?
the level of significance
The properties of a multinomial experiment include all of the following except
the probability of each outcome can change from trial to trial. The probability can NOT change
What is the central limit theorem?
the random variable being observed should be the sum or mean of many independent identically distributed random variables
The equation that describes how the dependent variable (y) is related to the independent variable (x) is called
the regression model
In a multiple regression model, the variance of the error term ε is assumed to be
the same for all values of the independent variable
To avoid the problem of not having access to Tables of F distribution with values given for the lower tail, the denominator of the test statistic should be the one with
the smaller sample variance
Standard error of the estimate
the square root of the mean square error, denoted by s. It is the estimate of o, the standard deviation of the error term e
Mean Square Error (MSE)
the unbiased estimate of the variance of the error term o2. It is denoted by MSE or s2
Dependent variable
the variable that is being predicted or explained. It is denoted by y
Independent variable
the variable that is doing the predicting or explaining. It is denoted by x
The assumptions for the multinomial experiment parallel those for the binomial experiment with the exception that for the multinomial
there are three or more outcomes per trial
If two variables, x and y, have a strong linear relationship, then
there may or may not be any causal relationship between x and y
A goodness of fit test is always conducted as a
upper-tail test
In a multiple regression model, the error term ε is assumed to be a random variable with a mean of
zero
