BNAD 277 Connect test 3
In a regression study where b2 = 3.67 and sb2= .92 whats the test statistic fortesting Ho = B2 = 1 versus Ha = B2 not = 1
(3.62 -1)/.92 = 2.9
In a regression B4 = -8.67 and Sb4 = 2.92. Calculate the value of the test stat for testing H0 = B4 = 0 versus Ha = B4 not = 0
-8.67-0/2.92 = -2.97
The summary information in regression output gives the value of the t test statistic and its associated p value for a two tailed test as -.762 and .452 respectively. Which of the following will be the p value if a one tailed test is specified?
.226
When determining whether there is a one to one relationship between x and y, the null hypothesis is
B1 = 1
In linear regression when determining if there is a negative linear relationship between x and y, what's the alternative hypothesis
B1<0
Null hypothesis to test whether the influence of x2 is identical to that of x3.
B2 = B3
Is SSTR for between or within
Between
If you're finding the critical value for H = or H not =, what to do you do for t?
Divide t alpha by 2
In a simple linear regression model, what is the notion for the random error term?
E
Null hypothesis to test if x2 and x3 are jointly significant
H0: B2 = B3 = 0
In a two way anova statistic that determines whether significant differences exist between the factor A means is calculated as
MSA/MSE
In a two way anova statistic that determines whether significant differences exist between the factor B means is calculated as
MSB/MSE
Teh test statistic for a test of joint significance is assumed to follow the F distribution and its value is calculated as
MSR/MSE
This ANOVA test is used to determine if differences exist between the ___ of three or more populations
Means
If the sample regression equation is found to be y hat = 10 + 2x, what is the observed value of y when x = 3?
Not enough information is provided to determine this. 16 would be the predicted value, not the observed
Multiple coefficient of determination is also
R squared
In two-way ANOVA without interaction, the SSE is calculated as
SST - (SSA+SSB)
If the simple regression equation is y hat = 15 + 5x which of hte following is the correct interpretation of 15?
The line crosses the y axis at y = 15
Which method ensures that the probability of a type 1 error equals alpha?
Tuckey's HSD method
When is a multiple regression model used?
When the researcher believes that two or more explanatory variables influence the response variable
Selling price of a car (y) using the age of the car (x) gave an intercept of 15 and coefficient of 'age' as -2? What is the estimated regression equation?
Y hat = 15 - 2x
Which of the following statements best defines a test statistic in a hypothesis test
a variable upon which the decision in hypothesis testing is based
In regression analysis, the response variable is also called
dependent variable
Tukey's HSD method uses _____ instead of ______ when compared to Fishers LSD method for pairwise comparisons
studentized range values, t values
In a two-way ANOVA, how many null hypotheses are tested?
2 or 3
In two-way ANOVA without interaction, we partition the total SST into ____ distinct components
3 SST= SSA + SSB + SSE
If regression is y hat = 30 + 5x what is estimate for the slope coefficient B1?
5
What is the simple linear regression model for the response variable of annual salary and explanatory variable of years of education
AS = B0 + B1ED +e
If the sample regression equation y hat = 15 - 5x, which of the following is the correct interpretation of the estimated slope coefficient?
For every unit increase in x, y will decrease, on average, by 5 units
For linear regression if we want to test if the influence of x2 is identical to that of x3, then the null hypothesis is
H0: B2 = B3
The competing hypotheses for a one-way ANOVA test that compares the means of three populations are defined as
H0: mu1=mu2=mu3 Ha: Not all populations means are equal
In a simple linear regression study, the R squared for model 1 is .9425 and the r squared for model 2 is .7248 which model should be used in predicting y?
Model 1
Do anova tests determine which population means differ?
No
If the interaction between two factors is significant, the next tests to be done are
None, more sophisticated techniques need to be used like regression analysis
In ANOVA testing, the ratio of the between-treatment variability to within-treatment variability is significantly greater than one, then we
Reject the null and conclude that not all the population means are equal
In two-way ANOVA without interaction, we partition the total sum of squares SST into the following components
SSA, SSB, and SSE
SSE equals (formula)
SST - (SSA + SSB)
In evaluating a regression model, why is a scatterplot a useful tool?
Scatterplot can be used to assess the linearity of the relationship
When constructing a Fisher confidence interval for the difference between two population means, we use the
Tdf distribution
Which of the following is NOT an assumption for performing a one-way ANOVA?
The population correlation coefficients indicate a strong linear relationship
Why is the stochastic model used in regression analysis in place of the deterministic model?
The relationship between the response and the explanatory variables is inexact
Which is true about test Ho: Pxy = 0?
The test statistic is assumed to follow the tdf distribution with n-2 df
Why are outliers sometimes removed from a data set?
They can distort the values of numerical measures
True or false: The one-way ANOVA test is based on the F df1,df2 distribution
True
In one-way ANOVA, within treatments variability is based on
a weighted sum of the sample variances of each treatment
What are symbols for the estimated model coefficients of the simplelinear regression equation
b0 and b1
Which coefficient is estimated simple regression equation indicated the change in the predicted value of y when x increases by one unit (B1, B0, b1, or b0)
b1
In practice, we use a stochastic model over a deterministic model because
certain variables that impact the response variable are not included in the model
In one way ANOVA, two independent estimates of the common population variance, sigma squares, are estimated. One estimate can be attributed to inherent differences between the c population while the other estimate can be attributed to
chance
If the alternative hypothesis is > or < what do you do to the p value
divide by 2
Tukey's HSD method ensures that the probability of a type 1 error equals alpha
for any number of pairwise comparisons
In a two way ANOVA test the sum of squares for Factor A is based on the sum of the squared differences between the mean for each level of factor A and the ____
grand mean
In regression analysis, explanatory variable is also called the
independent variable
When the value of the response variable is not uniquely determined by the explanatory variable, the relationship is said to be
inexact
In simple linear regression, the p-value of the F test identical to that of the t test because there is/are...
is only one slope coefficient being tested
In hypothesis tests about the population correlation coefficient, the alternative hypothesis of not equal to zero is used when testing whether two variable are
linearly related
The common approach to fitting a line to sample data in a scatterplot is to
minimize the value of the sum of the squared residuals
How many explanatory variables does a simple linear regression model have?
one
The graph is used to show the relationship between two variables is the
scatterplot
In one way ANOVA, error sum of squares (SSE) is the
sum of the weighted sample variances of each treatment
In one-way ANOVA, the sum of squares due to treatments (SSTR) is the
sum of the weighted squared differences between samples mean and the grand mean
If the interaction between two factors is not significant, the next tests to be done are
tests about the population means of factor A and/ or factor B
Covariance only indicates
the direction of the linear relationship, not the strength
The studentized range value q is dependent on
the significance level alpha, the number of populations c, and n-c.
In one-way ANOVA, between treatments variability is based on
the variability between sample means
Since ANOVA techniques were originally developed in connection with agricultural experiments, the term ____ is often used to identify the populations being examined for an ANOVA analysis
treatment
A two-way ANOVA test simultaneously examines the effect of ____ factors on the population mean
two
In order to determine if there is a difference between the means of 3 or more populations, we use
Analysis of variance
If two variables x and y have a covariance of 25 and two other variables x2 and y2 have covariance of 65 what conclusion can we draw about the relationship?
Each set shows a positive linear relationship
True or false? One-way ANOVA analysis does not require that all means differ from one another
True - One-way ANOVA analysis does not require that all means differ from one another, just that some of them differ
In regression, the two types of interval estimates concerning y are called the
confidence interval and prediction interval
When the response variable is uniquely determined by the explanatory variable, the relationship is
deterministic
One limitation of correction analysis is that it
does not imply causation
In a partial F test, the ____ is a complete model that imposes no restrictions on the coefficients
unrestricted model
In regression analysis, a confidence interval for the response variable is a range of values that, with a certain level of confidence, contains which of the following? (B0, e(x), B2, e(y)?)
E(y)
At the 5% significance level if P value of columns is .0701 do we reject?
No because .0701 is greater than .5. When P is less than alpha we reject the null
For which of the following situations is a simple linear regression model appropriate?
The response variable y is influenced by one explanatory variable
In a linear regression, which of the following is being tested if the null hypothesis states that B2 is greater than or equal to zero and the alternative hypothesis states that B2 is less than 0?
A negative linear relationship between X2 and y
In one-way ANOVA, two independent estimates of the common population variance, sigma squared, are estimated. These estimates are commonly referred to as
Between treatments variability and within treatments variability
In one-way ANOVA within treatments variability is based on the
variabiliy within each sample
WE apply Fisher's least significance difference method only when
we reject the null hypothesis of equal means
When do we use the alternative hypothesis: the population coefficient is less than zero?
When we test if two variables are negatively linearly related
For linear regression model, 99% confidence interval for B4 the slope coefficient of x4 is found to be (-2.5, 3.5) what is the interpretation
X4 is significant in explaining y at the 1% significance level. (Since the interval contains 0, x4 is not significant)
In a completely randomized ANOVA design, if there are an equal number of observations in each sample, then the design is ______
balanced
In a regression model, residual e is calculated as
y - y hat
If tdf test stat is =.762 and p value is .452 at 5% significance level is there a linear relationship between x and y?
No, because .452>.05 we do not reject H0; so x and y are not linearly related
In two-way ANOVA, if units within each block are randomly assigned to each of the treatments then the design of the experiment is referred to as a
randomized block design
Performing a one way ANOVA test, instead of performing a series of two-sample t tests ______ the risk of incorrectly rejecting the null
reduces
