Statistics for Business

In regression analysis, the variable that is being predicted is the a. response, or dependent, variable b. independent variable c. intervening variable d. is usually x

a.

In the case of an algebraic model for a straight line, if a value for the x variable is specified, then a. the exact value of the response variable can be computed b. the computed response to the independent value will always give a minimal residual c. the computed value of y will always be the best estimate of the mean response d. none of these alternatives is correct.

a.

Suppose that you have carried out a regression analysis where the total variance in the response is 133452 and the correlation coefficient was 0.85. The residual sums of squares is: a. 37032.92 b. 20017.8 c. 113434.2 d. 96419.07 e. 15% f. 0.15

a.

The coefficient of determination equals a. 0.6471 b. -0.6471 c. 0 d. 1

a.

SSE can never be a. larger than SST b. smaller than SST c. equal to 1 d. equal to zero

a. larger than SST

Assuming that the null hypothesis being tested by ANOVA is false, the probability of obtaining an F ratio that exceeds the value reported in the F table as the 95th percentile is: a. less than .05. b. equal to .05. c. greater than .05.

a. less than .05

If there is a very strong correlation between two variables then the correlation coefficient must be a. any value larger than 1 b. much smaller than 0, if the correlation is negative c. much larger than 0, regardless of whether the correlation is negative or positive d. None of these alternatives is correct.

b. much smaller than 0, if the correlation is negative

When conducting a one-way ANOVA, the _______ the between-treatment variability is when compared to the within-treatment variability, the _______ the value of FDATA will be tend to be. a. smaller, larger b. smaller, smaller c. larger, larger d. smaller, more random e. larger, more random

b. smaller, smaller

If two variables, x and y, have a very strong linear relationship, then a. there is evidence that x causes a change in y b. there is evidence that y causes a change in x c. there might not be any causal relationship between x and y d. None of these alternatives is correct.

c.

In a regression and correlation analysis if r 2 = 1, then a. SSE = SST b. SSE = 1 c. SSR = SSE d. SSR = SST

d.

SSE

sum of squared estimate of errors + example

If the correlation coefficient is a positive value, then the slope of the regression line a. must also be positive b. can be either negative or positive c. can be zero d. can not be zero

a.

In least squares regression, which of the following is not a required assumption about the error term ε? a. The expected value of the error term is one. b. The variance of the error term is the same for all values of x. c. The values of the error term are independent. d. The error term is normally distributed.

a.

Regression analysis was applied between $ sales (y) and $ advertising (x) across all the branches of a major international corporation. The following regression function was obtained. ! = 5000 + 7.25x If the advertising budgets of two branches of the corporation differ by $30,000, then what will be the predicted difference in their sales? a. $217,500 b. $222,500 c. $5000 d. $7.25

a.

Suppose the correlation coefficient between height (as measured in feet) versus weight (as measured in pounds) is 0.40. What is the correlation coefficient of height measured in inches versus weight measured in ounces? [12 inches = one foot; 16 ounces = one pound] a. 0.40 b. 0.30 c. 0.533 d. cannot be determined from information given e. none of these

a.

The error deviations within the SSE statistic measure distances: a. within groups b. between groups c. both (a) and (b) d. none of the above e. between each value and the grand mean

a.

The point estimate of y when x = 0.55 is a. 0.17205 b. 2.018 c. 1.0905 d. -2.018 e. -0.17205

a.

If you pooled all the individuals from all three lakes into a single group, they would have a standard deviation of: a. 1.257 (use q. 43) b. 1.580 c. 3.767 d. 14.19

a. 1.257

Assume the same variables as in question 28 above; height is measured in feet and weight is measured in pounds. Now, suppose that the units of both variables are converted to metric (meters and kilograms). The impact on the slope is: a. the sign of the slope will change b. the magnitude of the slope will change c. both a and b are correct d. neither a nor b are correct

b.

If the coefficient of determination is 0.81, the correlation coefficient a. is 0.6561 b. could be either + 0.9 or - 0.9 c. must be positive d. must be negative

b.

If the coefficient of determination is equal to 1, then the correlation coefficient a. must also be equal to 1 b. can be either -1 or +1 c. can be any value between -1 to +1 d. must be -1

b.

In a regression analysis if SSE = 200 and SSR = 300, then the coefficient of determination is a. 0.6667 b. 0.6000 c. 0.4000 d. 1.5000

b.

Regression analysis was applied to return rates of sparrowhawk colonies. Regression analysis was used to study the relationship between return rate (x: % of birds that return to the colony in a given year) and immigration rate (y: % of new adults that join the colony per year). The following regression equation was obtained. ! = 31.9 - 0.34x Based on the above estimated regression equation, if the return rate were to decrease by 10% the rate of immigration to the colony would: a. increase by 34% b. increase by 3.4% c. decrease by 0.34% d. decrease by 3.4%

b.

The coefficient of correlation a. is the square of the coefficient of determination b. is the square root of the coefficient of determination c. is the same as r-square d. can never be negative

b.

The data are the same as for question 4 above. The relationship between number of beers consumed (x) and blood alcohol content (y) was studied in 16 male college students by using least squares regression. The following regression equation was obtained from this study: != -0.0127 + 0.0180x Suppose that the legal limit to drive is a blood alcohol content of 0.08. If Ricky consumed 5 beers the model would predict that he would be: a. 0.09 above the legal limit b. 0.0027 below the legal limit c. 0.0027 above the legal limit d. 0.0733 above the legal limit

b.

The least squares estimate of b1 equals (see 37 GD) a. 0.923 b. 1.991 c. -1.991 d. -0.923

b.

You have carried out a regression analysis; but, after thinking about the relationship between variables, you have decided you must swap the explanatory and the response variables. After refitting the regression model to the data you expect that: a. the value of the correlation coefficient will change b. the value of SSE will change c. the value of the coefficient of determination will change d. the sign of the slope will change e. nothing changes

b.

If FDATA follows an F distribution with df1=4 and df2=5, what is the boundary value of F where P(FDATA < F) = 0.95? a. 0.05 b. 5.1922 c. 6.2561 d. 15.5291 e. 11.3919

b. 5.1922

You carried out an ANOVA on a preliminary sample of data. You then collected additional data from the same groups; the difference being that the sample sizes for each group were increased by a factor of 10, and the within-group variability has decreased substantially. Which of the following statements is NOT correct. a. The degrees of freedom associated with the error term has increased b. The degrees of freedom associated with the treatment term has increased c. SSE has decreased d. FDATA has changed e. FCRIT has changed

b. The degrees of Freedom associated with the treatment ter has increased

In regression, the equation that describes how the response variable (y) is related to the explanatory variable (x) is: a. the correlation model b. the regression model c. used to compute the correlation coefficient d. None of these alternatives is correct.

b. the regression model

The ______ sum of squares measures the variability of the observed values around their respective treatment means. a. treatment b. error c. interaction d. total

b.error

The ________ sum of squares measures the variability of the sample treatment means around the overall mean. a. treatment b. error c. interaction d. total

c. interaction

ANOVA: Analysis of variance is a statistical method of comparing the ________ of several populations. a. standard deviations b. variances c. means d. proportions e. none of the above

c. means

If the correlation coefficient is 0.8, the percentage of variation in the response variable explained by the variation in the explanatory variable is a. 0.80% b. 80% c. 0.64% d. 64%

d.

The least squares estimate of b0 equals a. 0.923 b. 1.991 c. -1.991 d. -0.923

d.

The sum of squares due to regression (SSR) is a. 1434 b. 505.98 c. 50.598 d. 928.02

d.

The value of FCRIT for this test is: a. 3.5874 (use q. 43) b. 3.8625 c. 3.9824 d. 4.2565

d. 4.2565

In regression analysis, the variable that is used to explain the change in the outcome of an experiment, or some natural process, is called a. the x-variable b. the independent variable c. the predictor variable d. the explanatory variable e. all of the above (a-d) are correct f. none are correct

e.

SSR or RSS

or residual sum of squares or sum of squared residuals

MSE

Mean Squared Error

SPSS

Statistical Package for the Social Sciences + example

You studied the impact of the dose of a new drug treatment for high blood pressure. You think that the drug might be more effective in people with very high blood pressure. Because you expect a bigger change in those patients who start the treatment with high blood pressure, you use regression to analyze the relationship between the initial blood pressure of a patient (x) and the change in blood pressure after treatment with the new drug (y). If you find a very strong positive association between these variables, then: a. there is evidence that the higher the patients initial blood pressure, the bigger the impact of the new drug. b. there is evidence that the higher the patients initial blood pressure, the smaller the impact of the new drug. c. there is evidence for an association of some kind between the patients initial blood pressure and the impact of the new drug on the patients blood pressure d. none of these are correct, this is a case of regression fallacy

d.

ANOVA was used to test the outcomes of three drug treatments. Each drug was given to 20 individuals. The MSE for this analysis was 16. What is the standard deviation for all 60 individuals sampled for this study? a. 6.928 b. 48 c. 16 d. 4

d. 4

The t test

+ add explanation + example

Chi-square

a common statistic used to analyze nominal and ordinal data to find differences between groups +example calculation with steps

correlation coefficient

a statistical index of the relationship between two things (from -1 to +1) +example calculation with steps

A fitted least squares regression line a. may be used to predict a value of y if the corresponding x value is given b. is evidence for a cause-effect relationship between x and y c. can only be computed if a strong linear relationship exists between x and y d. None of these alternatives is correct.

a.

As variability due to chance decreases, the value of F will a. increase b. stay the same c. decrease d. can't tell from the given information

a.

To determine whether the test statistic of ANOVA is statistically significant, it can be compared to a critical value. What two pieces of information are needed to determine the critical value? a. sample size, number of groups b. mean, sample standard deviation c. expected frequency, obtained frequency d. MSTR, MSE

a.

If the true means of the k populations are equal, then MSTR/MSE should be: a. more than 1.00 b. close to 1.00 c. close to 0.00 d. close to -1.00 e. a negative value between 0 and - 1 f. not enough information to make a decision

b.

In a regression analysis if r 2 = 1, then a. SSE must also be equal to one b. SSE must be equal to zero c. SSE can be any positive value d. SSE must be negative

b.

When the k population means are truly different from each other, it is likely that the average error deviation: a. is relatively large compared to the average treatment deviations b. is relatively small compared to the average treatment deviations c. is about equal to the average treatment deviation d. none of the above e. differ significantly between at least two of the populations

b.

If the sample means for each of k treatment groups were identical (yes, this is extremely unlikely), what would be the observed value of the ANOVA test statistic? a. 1.0 b. 0.0 c. A value between 0.0 and 1.0 d. A negative value e. Infinite

b. 0.0

The value of FDATA for this test is: a. 8.52 (use q. 43) b. 5.39 c. 2.00 d. 0.1854

b. 5.39

What is the function of a post-test in ANOVA? a. Determine if any statistically significant group differences have occurred. b. Describe those groups that have reliable differences between group means. c. Set the critical value for the F test (or chi-square).

b. Describe those groups that have reliable differences between group means. + add example

If FDATA = 5, the result is statistically significant a. Always b. Sometimes c. Never

b. Sometimes

Assuming no bias, the total variation in a response variable is due to error (unexplained variation) plus differences due to treatments (known variation). If a known variation is large compared to unexplained variation, which of the following conclusions is the best? a. There is no evidence for a difference in response due to treatments. b. There is evidence for a difference in response due to treatments. c. There is significant evidence for a difference in response due to treatments d. The treatments are not comparable. e. The cause of the response is due to something other than treatments.

b. There is evidence for a difference in response due to treatments.

A residual plot: a. displays residuals of the explanatory variable versus residuals of the response variable. b. displays residuals of the explanatory variable versus the response variable. c. displays explanatory variable versus residuals of the response variable. d. displays the explanatory variable versus the response variable. e. displays the explanatory variable on the x axis versus the response variable on the y axis.

c

If the MSE of an ANOVA for six treatment groups is known, you can compute a. df1 b. the standard deviation of each treatment group c. the pooled standard deviation d. b and c e. all answers are correct

c.

If the coefficient of determination is a positive value, then the regression equation a. must have a positive slope b. must have a negative slope c. could have either a positive or a negative slope d. must have a positive y intercept

c.

Larger values of r 2 (R2 ) imply that the observations are more closely grouped about the a. average value of the independent variables b. average value of the dependent variable c. least squares line d. origin

c.

This question is related to questions 4 and 21 above. The relationship between number of beers consumed (x) and blood alcohol content (y) was studied in 16 male college students by using least squares regression. The following regression equation was obtained from this study: != -0.0127 + 0.0180x Another guy, his name Dudley, has the regression equation written on a scrap of paper in his pocket. Dudley goes out drinking and has 4 beers. He calculates that he is under the legal limit (0.08) so he decides to drive to another bar. Unfortunately Dudley gets pulled over and confidently submits to a road-side blood alcohol test. He scores a blood alcohol of 0.085 and gets himself arrested. Obviously, Dudley skipped the lecture about residual variation. Dudley's residual is: a. +0.005 b. -0.005 c. +0.0257 d. -0.0257

c.

You obtained a significant test statistic when comparing three treatments in a one-way ANOVA. In words, how would you interpret the alternative hypothesis HA? a. All three treatments have different effects on the mean response. b. Exactly two of the three treatments have the same effect on the mean response. c. At least two treatments are different from each other in terms of their effect on the mean response. d. All of the above. e. None of the above.

c. At least two treatments are different from each other in terms of their effect on the mean response

If FDATA= 0.9, the result is statistically significant a. Always b. Sometimes c. Never

c. never

What is the appropriate interpretation of this test? a. Reject H0: All three fish populations have different mean weights. b. Reject H0: Exactly two of the three fish populations have the same means. c. Reject H0: At least one of the fish populations differs from the others in terms of their mean weight. d. Fail to reject H0: There is insufficient evidence for differences in mean weights of the fish from these three populations e. Fail to reject H0: The mean weights of the fish in these three populations are the same

c. Reject H0: At least one of the fish populations differs from the others in terms of their mean weight.

In one-way ANOVA, which of the following is used within the F-ratio as a measurement of the variance of individual observations? a. SSTR b. MSTR c. SSE c. MSE d. none of the above

c. SSE

Suppose the critical region for a certain test of the null hypothesis is of the form F > 9.48773 and the computed value of F from the data is 1.86. Then: a. H0 should be rejected. b. The significance level is given by the area to the left of 9.48773 under the appropriate F distribution. c. The significance level is given by the area to the right of 9.48773 under the appropriate F distribution. d. The hypothesis test is two-tailed e. None of these.

c. The significance level is given by the area to the appropriate F distribution.

The correlation coefficient is used to determine: a. A specific value of the y-variable given a specific value of the x-variable b. A specific value of the x-variable given a specific value of the y-variable c. The strength of the relationship between the x and y variables d. None of these

c. The strength of the relationship between the x and y variables

An investigator randomly assigns 30 college students into three equal size study groups (early morning, afternoon, late-night) to determine if the period of the day at which people study has an effect on their retention. The students live in a controlled environment for one week, on the third day of the experimental treatment is administered (study of predetermined material). On the seventh day the investigator tests for retention. In computing his ANOVA table, he sees that his MS within groups is larger than his MS between groups. What does this result indicate? a. An error in the calculations was made. b. There was more than the expected amount of variability between groups. c. There was more variability between subjects within the same group than there was between groups. d. There should have been additional controls in the experiment.

c. There was more variability between subjects within the same group than there was between groups.

When conducting an ANOVA, FDATA will always fall within what range? a. between negative infinity and infinity b. between 0 and 1 c. between 0 and infinity d. between 1 and infinity

c. between 0 and 1

The null hypothesis for this analysis is: (use q. 43) a. Not all the fish populations have the same mean. b. At least one of the fish populations has a different mean. c. µ1 = µ2 = µ3 d. µ1 = µ2 = µ3 = 0 e. None of these.

c. c. µ1 = µ2 = µ3 d. µ1 = µ2 = µ3 = 0

The relationship between number of beers consumed (x) and blood alcohol content (y) was studied in 16 male college students by using least squares regression. The following regression equation was obtained from this study: != -0.0127 + 0.0180x The above equation implies that: a. each beer consumed increases blood alcohol by 1.27% b. on average it takes 1.8 beers to increase blood alcohol content by 1% c. each beer consumed increases blood alcohol by an average of amount of 1.8% d. each beer consumed increases blood alcohol by exactly 0.018

c. each beer consumed increases blood alcohol by an average of amount of 1.8%

In ANOVA with 4 groups and a total sample size of 44, the computed F statistic is 2.33 In this case, the p-value is: a. exactly 0.05 b. less than 0.05 c. greater than 0.05 d. cannot tell - it depends on what the SSE is

c. greater than 0.05

Regression modeling is a statistical framework for developing a mathematical equation that describes how a. one explanatory and one or more response variables are related b. several explanatory and several response variables response are related c. one response and one or more explanatory variables are related d. All of these are correct.

c. one response and one or more explanatory variables are related

Assume that there is no overlap between the box and whisker plots for three drug treatments where each drug was administered to 35 individuals. The box plots for these data: a. provide no evidence for, or against, the null hypothesis of ANOVA b. represent evidence for the null hypothesis of ANOVA c. represent evidence against the null hypothesis of ANOVA d. can be very misleading, you should not be looking at box plots in this setting

c. represent evidence against the null hypothesis of ANOVA

A regression analysis between sales (in $1000) and price (in dollars) resulted in the following equation: ! = 50,000 - 8X The above equation implies that an a. increase of $1 in price is associated with a decrease of $8 in sales b. increase of $8 in price is associated with an increase of $8,000 in sales c. increase of $1 in price is associated with a decrease of $42,000 in sales d. increase of $1 in price is associated with a decrease of $8000 in sales

d.

In a study, subjects are randomly assigned to one of three groups: control, experimental A, or experimental B. After treatment, the mean scores for the three groups are compared. The appropriate statistical test for comparing these means is: a. the correlation coefficient b. chi square c. the t-test d. the analysis of variance

d.

In regression analysis, if the independent variable is measured in kilograms, the dependent variable a. must also be in kilograms b. must be in some unit of weight c. cannot be in kilograms d. can be any units

d.

Suppose you use regression to predict the height of a woman's current boyfriend by using her own height as the explanatory variable. Height was measured in feet from a sample of 100 women undergraduates, and their boyfriends, at Dalhousie University. Now, suppose that the height of both the women and the men are converted to centimeters. The impact of this conversion on the slope is: a. the sign of the slope will change b. the magnitude of the slope will change c. both a and b are correct d. neither a nor b are correct

d.

When the error terms have a constant variance, a plot of the residuals versus the independent variable x has a pattern that a. fans out b. funnels in c. fans out, but then funnels in d. forms a horizontal band pattern e. forms a linear pattern that can be positive or negative

d.

Which of the following is an assumption of one-way ANOVA comparing samples from three or more experimental treatments? a. All the response variables within the k populations follow a normal distributions. b. The samples associated with each population are randomly selected and are independent from all other samples. c. The response variable within each of the k populations have equal variances. d. All of the above.

d.

What would happen if instead of using an ANOVA to compare 10 groups, you performed multiple t-tests? a. Nothing, there is no difference between using an ANOVA and using a t-test. b. Nothing serious, except that making multiple comparisons with a t-test requires more computation than doing a single ANOVA. c. Sir Ronald Fischer would be turning over in his grave; he put all that work into developing ANOVA, and you use multiple t-tests d. Making multiple comparisons with a t-test increases the probability of making a Type I error.

d. Making multiple comparisons with a t-test increases the probability of making a Type I error.