SIMPLE LINEAR REGRESSION

AND CORRELATION

SECTIONS 1 - 2

MULTIPLE CHOICE QUESTIONS

In the following multiple-choice questions, please circle the correct answer.

1.The regression line [pic] = 3 + 2x has been fitted to the data points (4, 8), (2, 5), and (1, 2). The sum of the squared residuals will be: a. 7

b. 15

c. 8

d. 22

ANSWER:d

2.If an estimated regression line has a y-intercept of 10 and a slope of 4, then when x = 2 the actual value of y is: a. 18

b. 15

c. 14

d. unknown

ANSWER:d

3.Given the least squares regression line [pic]= 5 –2x:

a. the relationship between x and y is positive

b. the relationship between x and y is negative

c. as x increases, so does y

d. as x decreases, so does y

ANSWER:b

4.A regression analysis between weight (y in pounds) and height (x in inches) resulted in the following least squares line: [pic]= 120 + 5x. This implies that if the height is increased by 1 inch, the weight, on average, is expected to: a. increase by 1 pound

b. decrease by 1 pound

c. increase by 5 pounds

d. increase by 24 pounds

ANSWER:c

5.A regression analysis between sales (in $1000) and advertising (in $100) resulted in the following least squares line: [pic] = 75 +6x. This implies that if advertising is $800, then the predicted amount of sales (in dollars) is: a. $4875

b. $123,000

c. $487,500

d. $12,300

ANSWER:b

6.A regression analysis between sales (in $1000) and advertising (in $) resulted in the following least squares line: [pic] = 80,000 + 5x. This implies that an: a. increase of $1 in advertising is expected, on average, to result in an increase of $5 in sales b. increase of $5 in advertising is expected, on average, to result in an increase of $5,000 in sales c. increase of $1 in advertising is expected, on average, to result in an increase of $80,005 in sales d. increase of $1 in advertising is expected, on average, to result in an increase of $5,000 in sales ANSWER:d

7.Which of the following techniques is used to predict the value of one variable on the basis of other variables? a. Correlation analysis

b. Coefficient of correlation

c. Covariance

d. Regression analysis

ANSWER:d

8.The residual is defined as the difference between:

a. the actual value of y and the estimated value of y

b. the actual value of x and the estimated value of x

c. the actual value of y and the estimated value of x

d. the actual value of x and the estimated value of y

ANSWER:a

9.In the simple linear regression model, the y-intercept represents the: a. change in y per unit change in x

b. change in x per unit change in y

c. value of y when x = 0

d. value of x when y = 0

ANSWER:c

10.In the first order linear regression model, the population parameters of the y-intercept and the slope are estimated respectively, by: a. [pic] and [pic]

b. [pic] and [pic]

c. [pic] and [pic]

d. [pic] and [pic]

ANSWER:a

11.In the simple linear regression model, the slope represents the: a. value of y when x = 0

b. average change in y per unit change in x

c. value of x when y = 0

d. average change in x per unit change in y

ANSWER:b

12.In regression analysis, the residuals represent the:

a. difference between the actual y values and their predicted values b. difference between the actual x values and their predicted values c. square root of the slope of the regression line

d. change in y per unit change in x

ANSWER:a

13.In the first-order linear regression model, the population parameters of the y-intercept and the slope are, respectively, a. [pic] and [pic]

b. [pic] and [pic]

c. [pic] and [pic]

d. [pic] and [pic]

ANSWER:d

14.In a simple linear regression problem, the following...