Chapter 13
Linear Regression and Correlation
True/False
1. If a scatter diagram shows very little scatter about a straight line drawn through the plots, it indicates a
rather weak correlation.
Answer: False Difficulty: Easy Goal: 1
2. A scatter diagram is a chart that portrays the correlation between a dependent variable and an
independent variable.
Answer: True Difficulty: Easy Goal: 1 AACSB: AS
3. An economist is interested in predicting the unemployment rate based on gross domestic product.
Since the economist is interested in predicting unemployment, the independent variable is gross domestic
product.
Answer: True Difficulty: Medium Goal: 1 AACSB: REF
4. There are two variables in correlation analysis referred to as the dependent and determination
variables.
Answer: False Difficulty: Easy Goal: 1
5. Correlation analysis is a group of statistical techniques used to measure the strength of the relationship
(correlation) between two variables.
Answer: True Difficulty: Easy Goal: 2 AACSB: AS
6. The purpose of correlation analysis is to find how strong the relationship is between two variables.
Answer: True Difficulty: Easy Goal: 2
7. Originated by Karl Pearson about 1900, the coefficient of correlation describes the strength of the
relationship between two, interval or ratio-scaled variables.
Answer: True Difficulty: Easy Goal: 2
8. The coefficient of correlation, r, is often referred to as Spearman’s rho.
Answer: False Difficulty: Easy Goal: 2
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9. The coefficient of correlation r is often referred to as the Pearson product-moment correlation
coefficient.
Answer: True Difficulty: Easy Goal: 2
10. A correlation coefficient equal to –1 or +1 indicates perfect correlation.
Answer: True Difficulty: Easy Goal: 2
11. The strength of the correlation between two variables depends on the sign of the coefficient of
correlation.
Answer: False Difficulty: Easy Goal: 2
12. A coefficient of correlation, r, close to 0 (say, 0.08) shows that the relationship between two variables
is quite weak.
Answer: True Difficulty: Easy Goal: 2
13. Correlation coefficients of –0.91 and +0.91 represent relationships between two variables that have
equal strength but different directions.
Answer: True Difficulty: Easy Goal: 2 AACSB: REF
14. A coefficient of correlation of –0.96 indicates a very weak negative correlation.
Answer: False Difficulty: Easy Goal: 2
15. The coefficient of determination is the proportion of the total variation in the dependent variable Y
that is explained or accounted for by its relationship with the independent variable X.
Answer: True Difficulty: Easy Goal: 2
16. The coefficient of determination is found by taking the square root of the coefficient of correlation.
Answer: False Difficulty: Easy Goal: 2
17. If the coefficient of correlation is –0.90, the coefficient of determination is –0.81.
Answer: False Difficulty: Medium Goal: 2
18. If the coefficient of correlation is –0.50, the coefficient of determination is +0.25.
Answer: True Difficulty: Medium Goal: 2
19. If the coefficient of correlation is 0.68, the coefficient of determination is 0.4624.
Answer: True Difficulty: Medium Goal: 2
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20. The correlation coefficient is the proportion of total variation in Y that is explained by X.
Answer: False Difficulty: Easy Goal: 2
21. The coefficient of determination is the proportion of total variation in Y that is not explained by X.
Answer: False Difficulty: Easy Goal: 2
22. The coefficient of determination is the proportion of total variation in Y that is explained by X.
Answer: True Difficulty: Easy Goal: 2
23. Pearson’s product-moment correlation coefficient, r, requires that the data be interval or ratio scaled,
such as incomes and weights.
Answer: True Difficulty: Easy Goal: 2
24. The standard error of estimate measures the accuracy of our prediction.
Answer: True Difficulty: Medium Goal: 2
25. Pearson’s coefficient of correlation can be used if the data is nominally scaled.
Answer: False Difficulty: Easy Goal: 2
26. The coefficient of determination can only be positive.
Answer: True Difficulty: Easy Goal: 2
27. If the coefficient of determination is expressed as a percent, its value is between 0% and 100%.
Answer: True Difficulty: Easy Goal: 2
28. A t test is used to test the significance of the coefficient of correlation.
Answer: True Difficulty: Medium Goal: 3
29. To test the significance of Pearson’s r, we use the standard normal z distribution.
Answer: False Difficulty: Medium Goal: 3
30. When testing the strength of the relationship between two variables, the null hypothesis is:
0ρ:HO
.
Answer: True Difficulty: Medium Goal: 3
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31. When testing the strength of the relationship between two variables, the alternate hypothesis is:
0ρ:HO
.
Answer: True Difficulty: Medium Goal: 3
32. The basic question in testing the significance of ρ (rho) is to make a statistical inference about the
true relationship between two variables.
Answer: True Difficulty: Medium Goal: 3 AACSB: AS
33. One assumption underlying linear regression is that the Y values are statistically dependent. This
means that in selecting a sample, the Y values chosen, for a particular X value, depend on the Y values for
any other X value.
Answer: False Difficulty: Easy Goal: 4 AACSB: AS
34. The technique used to measure the strength of the relationship between two variables using the
coefficient of correlation and the coefficient of determination is called regression analysis.
Answer: False Goal: 4
35. A regression equation may be determined using a mathematical method called the least squares
principle.
Answer: True Difficulty: Easy Goal: 4
36. A regression equation found using the least squares principle is the best-fitting line because the sum
of the squares of the vertical deviations between the actual and estimated values is minimized.
Answer: True Difficulty: Easy Goal: 4 AACSB: REF
37. The least squares technique minimizes the sum of the squares of the vertical distances between the
actual Y values and the predicted values of Y.
Answer: True Difficulty: Easy Goal: 4 AACSB: REF
38. The values of a and b in the regression equation are called the regression coefficients.
Answer: True Difficulty: Easy Goal: 4 AACSB: REF
39. One assumption underlying linear regression is that for each value of X there is a group of Y values
that is normally distributed.
Answer: True Difficulty: Medium Goal: 4
40. In order to visualize the regression equation line, we can draw a scatter diagram.
Answer: True Difficulty: Easy Goal: 4
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41. A regression equation is a mathematical equation that defines the relationship between two variables.
Answer: True Difficulty: Easy Goal: 4
42. The equation for a straight line going through the plots on a scatter diagram is called a regression
equation. It is alternately called an estimating equation and a predicting equation.
Answer: True Difficulty: Easy Goal: 4
43. The regression equation is used to estimate a value of the dependent variable Y based on a selected
value of the independent variable X.
Answer: True Difficulty: Medium Goal: 4
44. In regression analysis, the predicted value of
ˆ
Y
rarely agrees exactly with the actual Y value, i.e., we
expect some prediction error.
Answer: True Difficulty: Medium Goal: 4
45. Trying to predict weekly sales with a standard error of estimate of $1,955, we would conclude that 68
percent of the predictions would not be off more than $1,955, 95 percent would not be off by more
