Question

8) (3 pts) Schlitz has been told that every thousand dollars added to the median household income should increase the page cost by less than $750. She wishes to test whether the regression provides convincing evidence to reject this claim. Therefore, she should test a) H0: βINCOME = -0.750 versus Ha: βINCOME < -0.750 b) H0: βINCOME = 0.750 versus Ha: βINCOME < 0.750 c) H0: βINCOME = -0.750 versus Ha: βINCOME ≠ -0.750 d) H0: βINCOME = 0.750 versus Ha: βINCOME ≠ 0.750 e) H0: βINCOME = -0.750 versus Ha: βINCOME > -0.750 f) H0: βINCOME = 0.750 versus Ha: βINCOME > 0.750 9) (3 pts) Schlitz is intrigued by the number 16.9149, which appears near the top of the regression output and is labeled as “Standard Error.” Which is the most accurate interpretation of this number? (choose one) a) 16.9149% of the variation in the PAGECOST variable can be explained by this regression. b) It measures the precision with which the regression has estimated the intercept coefficient. c) It is the standard deviation of the population parameter μ. d) It is the standard deviation of the residuals. 10) (2 pts) Schlitz is thinking of adding another explanatory variable to her regression (the actual numeric ratings from Media Journal). How will the standard error of the estimate change? (choose one): a) It will increase. b) It will decrease. c) It may increase or may decrease. d) It will definitely stay the same. 11) (3 pts) Suppose Schlitz ran a second regression of PAGECOST versus INCOME and RATING. Consider a plot of PAGECOST versus INCOME in which we represent the “above average rating” predictions with a red line and the “below average rating” predictions with a white line. Which is true? a) The intercepts of the red line and white line will be the same, but the slopes might be different. b) The slopes of the red line and the white line will be the same, but the intercepts might be different. c) The red and white lines will be identical. d) The red and white lines will have different intercepts and different slopes. 12) (1 pts) Suppose Schlitz runs a simple regression of PAGECOST versus DIE, where for DIE she enters the outcomes of 55 rolls of a 6-sided die. What is the probability that the resulting F-test indicates a significant regression at the 5% level? a) 0.00 b) 0.01 c) 0.05 d) 0.10 e) None of the above 13) (2 pts) Schlitz believes that using the “standard error of the estimate” to calculate an approximate prediction interval gives an under-estimate of the length of the true interval. This is a) True b) False c) Sometimes true and sometimes false. 14) (3 pts) If Schlitz’s regression suffers from multi-collinearity, it means that a) Residual errors are highly correlated with an explanatory variable b) An explanatory variable is highly correlated with the dependent variable c) Two or more explanatory variables are highly correlated with each other. d) Residual errors are highly correlated with the dependent variable e) There is a problem with covariation 15. (3 pts) A correlation analysis between sales and sales training scores results in correlation coefficient, R = +0.98. Which of the following best interprets the relationship between sales and sales training? a) 98% of the salespeople taking the test have higher sales b) the correlation between sales and sales training is very weak and insignificant c) the correlation between sales and sales training is strong and positive d) 98% of the variation in sales is explained by variations in sales training scores e) none of the above 16. (2 pts) Which of the following best describes the sampling distribution of the mean? a) it is the frequency distribution for all of the elements of the population b) it is a probability distribution of the means of varying sample sizes for relevant populations c) it is a probability distribution of the means of all possible samples of a given size drawn from a particular population d) none of the above e) (A), (B) and (C)

Answer 1

8) (3 pts) Schlitz has been told that every thousand dollars added to the median household income should increase the page cost by less than $750. She wishes to test whether the regression provides convincing evidence to reject this claim.

Therefore, she should test

We should note that there would be an increase in the page cost .Hence the null hypothesis should be a positive 0.750.

Next we should test whether the increase is 0.750 or lesser than 0.750 .Hence alternative hypothesis should be <0.750.So the correct choice is b).

b) H0: βINCOME = 0.750 versus Ha: βINCOME < 0.750

9) (3 pts) Schlitz is intrigued by the number 16.9149, which appears near the top of the regression output and is labeled as “Standard Error.” Which is the most accurate interpretation of this number?

As .,Standard error is a statistical term that measures the accuracy with which a sample represents a population.

. b) It measures the precision with which the regression has estimated the intercept coefficient.

This is the most accurate interpretation .

10) (2 pts) Schlitz is thinking of adding another explanatory variable to her regression (the actual numeric ratings from Media Journal). How will the standard error of the estimate change?

This question can be answered by defining R².As R² or the coefficient of determination i.e explained variation/total variation gives us how close the estimate fit is to the actual fit.As we keep on adding MUTUALLY INDEPENDENT variables the R² increases and hence standard error estimate goes on decreasing as accuracy of the model increases.Note that if the variables are not independent collinearity may exist which may cause standard error to increase.

b) It will decrease

11) (3 pts) Suppose Schlitz ran a second regression of PAGECOST versus INCOME and RATING. Consider a plot of PAGECOST versus INCOME in which we represent the “above average rating” predictions with a red line and the “below average rating” predictions with a white line. Which is true?

The model here would be

PAGECOST = A*INCOME+B*RATING +C, where A and B are regression coefficients of income and rating respectively and C is the intercept.

For Y (Pagecost) vs. X₁ (Income) we plot a graph and above average rating where red line represents above average rating and white line is below average rating

a) The intercepts of the red line and white line will be the same, but the slopes might be different.

The reason is that C i.e regressor of constant would be same in both cases but B would vary depending on the rating hence model Y would have same intercept but different regressor.

12) (1 pts) Suppose Schlitz runs a simple regression of PAGECOST versus DIE, where for DIE she enters the outcomes of 55 rolls of a 6-sided die. What is the probability that the resulting F-test indicates a significant regression at the 5% level?

As pagecost Y is indepednent of the regressor die the probability that F test would indicate a significant regressor is 0

a) 0.00

13) (2 pts) Schlitz believes that using the “standard error of the estimate” to calculate an approximate prediction interval gives an under-estimate of the length of the true interval.

This is false as any confidence interval can be predicted by

( (mean of estimate)-Z_alpha*(S,E of estimate) ,(mean of estimate)+Z_alpha*(S,E of estimate))

This is b)false

14) (3 pts) If Schlitz’s regression suffers from multi-collinearity, it means that

c) Two or more explanatory variables are highly correlated with each other.

15. (3 pts) A correlation analysis between sales and sales training scores results in correlation coefficient, R = +0.98. Which of the following best interprets the relationship between sales and sales training?

As R squared is the ratio of explained variation and total variation ,hence

d) 98% of the variation in sales is explained by variations in sales training scores

16. (2 pts) Which of the following best describes the sampling distribution of the mean?

a) it is the frequency distribution for all of the elements of the population

b) it is a probability distribution of the means of varying sample sizes for relevant populations

c) it is a probability distribution of the means of all possible samples of a given size drawn from a particular population

Answer is :

e) (A), (B) and (C) as all describe the sampling distribution.Note that frequency distribution is a population distribution when weights are the respective probabilities.