MIS 175 Section 4 - Second Midterm Examination



DS 101 Version R082 – Sample Exam Questions

Simple Linear Regression Questions

1. In regression analysis, the model in the form [pic] is called

|a. |regression equation |

|b. |correlation equation |

|c. |estimated regression equation |

|d. |regression model |

2. The mathematical equation relating the independent variable to the expected value of the dependent variable; that is, E(y) = β0 + β1x, is known as

|a. |regression equation |

|b. |correlation equation |

|c. |estimated regression equation |

|d. |regression model |

3. The model developed from sample data that has the form of [pic] is known as

|a. |regression equation |

|b. |correlation equation |

|c. |estimated regression equation |

|d. |regression model |

4. In regression analysis, the unbiased estimate of the variance is

|a. |coefficient of correlation |

|b. |coefficient of determination |

|c. |mean square error |

|d. |slope of the regression equation |

5. The interval estimate of the mean value of y for a given value of x is

|a. |prediction interval estimate |

|b. |confidence interval estimate |

|c. |average regression |

|d. |x versus y correlation interval |

6. The standard error is the

|a. |t-statistic squared |

|b. |square root of SSE |

|c. |square root of SST |

|d. |square root of MSE |

7. If MSE is known, you can compute the

|a. |r square |

|b. |coefficient of determination |

|c. |standard error |

|d. |all of these alternatives are correct |

8. In regression analysis, 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. |

9. Larger values of 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 |

10. In a regression and correlation analysis if r2 = 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 |

11. In a regression and correlation analysis if r2 = 1, then

|a. |SSE = SST |

|b. |SSE = 1 |

|c. |SSR = SSE |

|d. |SSR = SST |

12. 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 |

13. In regression analysis, if the independent variable is measured in pounds, the dependent variable

|a. |must also be in pounds |

|b. |must be in some unit of weight |

|c. |cannot be in pounds |

|d. |can be any units |

14. A regression analysis between sales (in $1000) and price (in dollars) resulted in the following equation

[pic] = 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 |

15. Regression analysis was applied between sales (in $1000) and advertising (in $100) and the following regression function was obtained.

[pic] = 500 + 4 X

Based on the above estimated regression line if advertising is $10,000, then the point estimate for sales (in dollars) is

|a. |$900 |

|b. |$900,000 |

|c. |$40,500 |

|d. |$505,000 |

Multiple Regression Questions

1. The mathematical equation relating the expected value of the dependent variable to the value of the independent variables, which has the form of E(y) = [pic] is

|a. |a simple linear regression model |

|b. |a multiple nonlinear regression model |

|c. |an estimated multiple regression equation |

|d. |a multiple regression equation |

2. The estimate of the multiple regression equation based on the sample data, which has the form of E(y) = [pic]

|a. |a simple linear regression model |

|b. |a multiple nonlinear regression model |

|c. |an estimated multiple regression equation |

|d. |a multiple regression equation |

3. The mathematical equation that explains how the dependent variable y is related to several independent variables x1, x2, ..., xp and the error term ε is

|a. |a simple nonlinear regression model |

|b. |a multiple regression model |

|c. |an estimated multiple regression equation |

|d. |a multiple regression equation |

4. A measure of the effect of an unusual x value on the regression results is called

|a. |Cook’s D |

|b. |Leverage |

|c. |odd ratio |

|d. |unusual regression |

5. In a multiple regression model, the error term ε is assumed to be a random variable with a mean of

|a. |zero |

|b. |-1 |

|c. |1 |

|d. |any value |

6. A regression model in which more than one independent variable is used to predict the dependent variable is called

|a. |a simple linear regression model |

|b. |a multiple regression model |

|c. |an independent model |

|d. |None of these alternatives is correct. |

7. A multiple regression model has the form

[pic]

As x1 increases by 1 unit (holding x2 constant), y is expected to

|a. |increase by 9 units |

|b. |decrease by 9 units |

|c. |increase by 2 units |

|d. |decrease by 2 units |

8. A multiple regression model has the form

[pic]

As X increases by 1 unit (holding W constant), Y is expected to

|a. |increase by 11 units |

|b. |decrease by 11 units |

|c. |increase by 6 units |

|d. |decrease by 6 units |

Exhibit 15-2

A regression model between sales (Y in $1,000), unit price (X1 in dollars) and television advertisement (X2 in dollars) resulted in the following function:

[pic]

For this model SSR = 3500, SSE = 1500, and the sample size is 18.

9. Refer to Exhibit 15-2. The coefficient of the unit price indicates that if the unit price is

|a. |increased by $1 (holding advertising constant), sales are expected to increase by $3 |

|b. |decreased by $1 (holding advertising constant), sales are expected to decrease by $3 |

|c. |increased by $1 (holding advertising constant), sales are expected to increase by $4,000 |

|d. |increased by $1 (holding advertising constant), sales are expected to decrease by $3,000 |

10. Refer to Exhibit 15-2. The coefficient of X2 indicates that if television advertising is increased by $1 (holding the unit price constant), sales are expected to

|a. |increase by $5 |

|b. |increase by $12,000 |

|c. |increase by $5,000 |

|d. |decrease by $2,000 |

Exhibit 15-4

a. [pic]

b. [pic]

c. [pic]

d. [pic]

11. Which equation describes the multiple regression model?

|a. |Equation A |

|b. |Equation B |

|c. |Equation C |

|d. |Equation D |

12. Which equation gives the estimated regression line?

|a. |Equation A |

|b. |Equation B |

|c. |Equation C |

|d. |Equation D |

13. Which equation describes the multiple regression equation?

|a. |Equation A |

|b. |Equation B |

|c. |Equation C |

|d. |Equation D |

Exhibit 15-5

Below you are given a partial Minitab output based on a sample of 25 observations.

| |Coefficient |Standard Error |

|Constant |145.321 |48.682 |

|X1 |25.625 |9.150 |

|X2 |-5.720 |3.575 |

|X3 |0.823 |0.183 |

14. Refer to Exhibit 15-5. The estimated regression equation is

|a. |[pic] |

|b. |[pic] |

|c. |[pic] |

|d. |[pic] |

15. Refer to Exhibit 15-5. The interpretation of the coefficient on X1 is that

|a. |a one unit change in X1 will lead to a 25.625 unit change in Y |

|b. |a one unit change in X1 will lead to a 25.625 unit increase in Y when all other variables are held constant |

|c. |a one unit change in X1 will lead to a 25.625 unit increase in X2 when all other variables are held constant |

|d. |It is impossible to interpret the coefficient. |

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