# 10.10: Chapter 10 Solutions

$$\newcommand{\vecs}{\overset { \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}{\| #1 \|}$$ $$\newcommand{\inner}{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}{\| #1 \|}$$ $$\newcommand{\inner}{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$$$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$

1. c

2. A measure of the degree to which variation of one variable is related to variation in one or more other variables. The most commonly used correlation coefficient indicates the degree to which variation in one variable is described by a straight line relation with another variable.

Suppose that sample information is available on family income and Years of schooling of the head of the household. A correlation coefficient = 0 would indicate no linear association at all between these two variables. A correlation of 1 would indicate perfect linear association (where all variation in family income could be associated with schooling and vice versa).

3. a. 81% of the variation in the money spent for repairs is explained by the age of the auto

4. b. 16

5. The coefficient of determination is $$r2$$ with $$0 \leq r2 \leq 1$$, since $$-1 \leq r \leq 1$$.

6. True

7. d. on a scale from -1 to +1, the degree of linear relationship between the two variables is +.10

8. d. there exists no linear relationship between $$X$$ and $$Y$$

9. Approximately 0.9

10. d. neither of the above changes will affect $$r$$.

12. c. those who score low on one test tend to score low on the other.

13. False. Since $$H_{0} : \beta=-1$$ would not be rejected at $$\alpha=0.05$$, it would not be rejected at $$\alpha=0.01$$.

14. True

15. d

16. Some variables seem to be related, so that knowing one variable's status allows us to predict the status of the other. This relationship can be measured and is called correlation. However, a high correlation between two variables in no way proves that a cause-and-effect relation exists between them. It is entirely possible that a third factor causes both variables to vary together.

17. True

19. d. there is a perfect negative relationship between $$Y$$ and $$X$$ in the sample.

20. b. low

21. The precision of the estimate of the $$Y$$ variable depends on the range of the independent ($$X$$) variable explored. If we explore a very small range of the $$X$$ variable, we won't be able to make much use of the regression. Also, extrapolation is not recommended.

23.

1. $$80+1.5 * 4=86$$
2. No. Most business statisticians would not want to extrapolate that far. If someone did, the estimate would be 110, but some other factors probably come into play with 20 years.

24. d. one quarter

25. b. $$r = −.77$$

10.10: Chapter 10 Solutions is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.