1) In regression, an independent variable is sometimes called a response variable.

    TRUE                      FALSE

2) The dependent variable is also called the response variable.

    TRUE                      FALSE

3) There is no relationship between variables unless the data points lie in a straight line.

    TRUE                      FALSE

4) In regression, there is random error that can be predicted.

    TRUE                      FALSE

5) Estimates of the slope, intercept, and error of a regression model are found from sample data.

    TRUE                      FALSE

6) Error is the difference in the actual value and the predicted value.

    TRUE                      FALSE

7) The regression line minimizes the sum of the squared errors.

    TRUE                      FALSE

8) The SSE measures the total variability in the independent variable about the regression line.

    TRUE                      FALSE

9) The SSR indicates how much of the total variability in the dependent variable is explained by the regression model.

    TRUE                      FALSE

10) The coefficient of determination takes on values between -1 and + 1.

    TRUE                      FALSE

11) The regression model assumes the errors are normally distributed.

    TRUE                      FALSE

12) The standard error of the estimate is also called the variance of the regression.

    TRUE                      FALSE

13) Which of the following equalities is correct?





E) SSE = Actual Value – Predicted Value

14) If computing a causal linear regression model of Y = a + bX and the resultant r2 is very near zero, then one would be able to conclude that

A) Y = a + bX is a good forecasting method.

B) Y = a + bX is not a good forecasting method.

C) a multiple linear regression model is a good forecasting method for the data.

D) a multiple linear regression model is not a good forecasting method for the data.

E) None of the above

15) The correlation coefficient resulting from a particular regression analysis was 0.25.  What was the coefficient of determination?

A) 0.5

B) -0.5

C) 0.0625

D) There is insufficient information to answer the question.

E) None of the above

16) Which of the following represents the underlying linear model for hypothesis testing?

A) Y = b0 + b1 X + ε

B) Y = b0 + b1 X

C) Y = β0 + β1 X + ε

D) Y = β0 + β1 X

E) None of the above


Use the following information to answer questions number 17 and 18. Show how you derive the answer!

Y-bar = 10

X-bar = 7

X-Variance = 13

X and Y Covariance = 15.5

Y = b0 + b1X

17. Calculate the b1

18. Calculate the b0

Use the following information to answer questions 19 to 23

SST = 32.5

SSE = 10.5

SSR = 22

n = 6

k = 1

á = 0.05

19. Calculate the r2

r2 = 1 – SSE/SST = 1 – 10.5 / 32.5 = 1 – 0.32 = 0.67

20. What is the interpretation of your calculated r2?

The coefficient of determination, denoted R² or r² and pronounced “R squared”, is the proportion of the variation in the dependent variable that is predictable from the independent variable.

The coefficient of determination is a measurement used to explain how much variability of one factor can be caused by its relationship to another related factor.

This would indicate that 67% of the variance of the dependent variable being studied is explained by the variance of the independent variable.

21. Calculate the r

r = Square root of r2 = √0.67 = 0.81

22. Calculate the s2

23. Calculate the s

24. Calculate the F-statistics

25. Should we reject the null hypothesis or not? Why?

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