1. 1) A residual:
a) is the amount of variation explained by the LSRL of y on x
b) is how much an observed y-value differs from a predicted y-value
c) predicts how well x explains y
d) is the total variation of the data points
e) should be smaller than the mean of y

2. 2) Consider data set A: (2,8), (3,6), (4,9), and (5,9)
2) Consider data set A: (2,8), (3,6), (4,9), and (5,9). Which of the following is the proper interpretation of the r-square value?
a) there is a 30% increase in the variation in the data set
b) 30% of the variation in x-values can be explained by the LSRL of the y-values
c) 30% of the variation in y-values can be explained by the LSRL of the x-values
d) you have reduced the total variation by 70%
e) 70% of the variation in y-values can be explained by the LSRL of the x-values

3. 3) Which of the following statements about residuals is true?
I. For a perfect linear relationship the residuals are all zero.
II. The mean of the residuals can be positive.
III. A positive residual indicate the linear model is overestimating the actual value
A) I and II
B) I and III
C) II and III
D) I, II, and III
E) None of the above gives the complete set of true responses.

4. 4) The scatter-plot of residuals vs
4) The scatter-plot of residuals vs. observed x-values looks the same as the scatter-plot of residuals vs. observed y-values
a) true
b) false

5. 5) Which of the following is true when the observed data point falls below the least squares regression line?
the residual for this point is positive
the residual for this point is negative
the observed value of y is greater than the predicted value of y
I only
II only
I and III
II and III
e) all of the statements are false

6. 6) A coefficient of determination is found to be 64%
6) A coefficient of determination is found to be 64%. Which of these statements is true?
64% of the variation in the variables is accounted for in the linear relationship
36% of the variation in the variables is not accounted for in the linear relationship
the correlation coefficient is 0.8
a) I only
b) II only
c) III only
d) I and II
e) I and III

7. 7) Suppose the regression line for a set of data, y = 4x + b, passes through point (3, 10). If and are the sample means of the x- and y-values, respectively, then = A) B) C) D)
E) There is not enough information given

8. 8) The goal of a least squares regression line is to compute a line that:
a) connects all the bivariate data points in a scatterplot
b) collects all the residuals shown in a scatterplot
c) minimizes the sum of the observed values of x and y
d) minimizes the sum of the squared residuals
e) none of the above

9. 9) The equation of the least squares regression line for a set of given points is
What is the residual for the point (4, 7)?
2.78
-2.78
4.22
-4.22
(E) None of these

10. 10) Suppose the correlation between two variables is r =. 23
10) Suppose the correlation between two variables is r = What will the new correlation be if .14 were added to all values of the x-variable, every value of the y-variable is doubled, and the two variables are interchanged?
(A) .23
.37
.74
-.23
(E) .46

11. 11) A simple random sample of 50 families produced these statistics:
number of children in family: = 2.1, = 1.4 annual gross income: = 34,250, = 10,540
r = 0.75
The linear regression equation relating these variables, based on these data, is
income = 5,646(number of children) + 22,392
(B) income = 34, (number of children)
(C) income = (number of children) – 1.312
(D) number of children = 5,646(income) + 22,392
(E) None of these

12. 12) Using least-squares regression, I determine that the logarithm (base 10) of the population, y, of a country is approximately described by the equation
where x represents the year. Based on this equation, the population of the country in the year 2000 should be about
6.5
(B) 665
(C) 6,665
(D) 2,000,000
(E) 3,162,278