Question
1. Given a set of ordered pairs (x, y) so that sx = 1.6, sy = 0.75, r = 0.55. What is the slope of the least-square regression line for these data?
a. 1.82
b. 1.17
c. 2.18
d. 0.26
e. 0.78
Answer/Explanation
Markscheme: d
\(b=r.\frac{s_y}{s_x}=(0.55)(\frac{0.75}{1.6})=0.26\)
Question
2. 
The regression line for the two-variable dataset given above is \(\hat{y}\) = 2.35 + 0.86x. What is the value of the residual for the point whose x-value is 29?
a. 1.71
b. -1.71
c. 2.29
d. 5.15
e. -2.29
Answer/Explanation
Markscheme: e
The value of a residual = actual value – predicted value = 25 – [2.35 + 0.86(29)] = -2.29.
Question
3. A study found a correlation of r = -0.58 between hours per week spent watching television and hours per week spent exercising. That is, the more hours spent watching television, the less hours spent exercising per week. Which of the following statements is most accurate?
a. About one-third of the variation in hours spent exercising can be explained by hours spent watching television.
b. A person who watches less television will exercise more.
c. For each hour spent watching television, the predicted decrease in hours spent exercising is 0.58 hrs.
d. There is a cause-and-effect relationship between hours spent watching television and a decline in hours spent exercising. e. 58% of the hours spent exercising can be explained by the number of hours watching television.
Answer/Explanation
Markscheme: a
r2 = (-0.58)2 = 0.3364. This is the coefficient of determination, which is the proportion of the variation in the response variable that is explained by the regression on the independent variable. Thus, about one-third (33.3%) of the variation in hours spent exercising can be explained by hours spent watching teleision.
(b) is incorrect since correlation does not imply causation. (c) would be correct if b = –0.58, but there is no obvious way to predict the response value from the explanatory value just by knowing r. (d) is incorrect for the same reason (b) is incorrect. (e) is incorrect since r, not r2, is given. In this case r2 = 0.3364, which makes (a) correct.
Question
4. A response variable appears to be exponentially related to the explanatory variable. The natural logarithm of each y-value is taken and the least-squares regression line is found to be In (\(\hat{y}\) = 1.64 – 0.88x. Rounded to two decimal places, what is the predicted value of y when x = 3.1?
a. -1.09
b. -0.34
c. 0.34
d. 0.082
e. 1.09
Answer/Explanation
Markscheme: c
ln( y) = 1.64 – 0.88(3.1) = -1.088 ⇒ y = e-1.088 = 0.337. 5.
Question
5. Consider the following residual plot:
Which of the following statements is (are) true?
I. The residual plot indicates that a line is a reasonable model for the data.
II. The residual plot indicates that there is no relationship between the data.
III. The correlation between the variables is probably non-zero. a. I only
b. II only
c. I and III only
d. II and III only
e. I and II only
Answer/Explanation
Markscheme: c
The pattern is more or less random about 0, which indicates that a line would be a good model for the data. If the data are linearly related, we would expect them to have a non-zero correlation.