The Practice of Statistics, 4th Edition, a combination of Exams A,B & C
Question 1
1.
Question 2
2.
Question 3
3.
Question 4
4.
A least-squares regression line for predicting weights of basketball players on the basis of their heights produced the residual plot below.
Question 5
5.
One concern about the depletion of the ozone layer is that the increase in ultraviolet (UV) light will decrease crop yields. An experiment was conducted in a green house where soybean plants were exposed to varying levels of UV, measured in Dobson units. At the end of the experiment the yield (kg) was measured. A regression analysis was performed with the following results:
Question 6
6.
Question 7
7.
Question 8
8.
Question 9
9.
Question 10
10.
Part 2: Free Response
Show all your work. Indicate clearly the methods you use, because you will be graded on the correctness of your methods as well as on the accuracy and completeness of your results and explanations.
A certain psychologist counsels people who are getting divorced. A random sample of ten of her patients provided the data in the following scatterplot, where x = number of years of courtship before marriage, and y = number of years of marriage before divorce.
Question 11
11.
Describe what the scatterplot reveals about the relationship between length of courtship and length of marriage.
Question 12
12.
Suppose a new point at (4.5, 8), that is, years of courtship = 4.5 and years of marriage = 8, were added to the plot. What effect, if any, will this new point have on the correlation between courtship duration and marriage duration? Explain.
Below is the computer output for the regression of length of marriage versus length of courtship.
Question 13
13.
What is the slope of the regression line? Interpret the slope in the context of this problem.
Question 14
14.
Explain what the quantity S = 2.74982 measures in the context of this problem.
A community college announces that the correlation between college entrance exam grades and scholastic achievement was found to be –1.08. On the basis of this you would tell the college that
the entrance exam is a good predictor of success
the exam is a poor predictor of success.
students at this school are underachieving.
the college should hire a new statistician.
students who do best on this exam will be poor students.
In a statistics course, a linear regression equation was computed to predict the final-exam score from the score on the first test. The equation was yˆ = 10 + 0.9x where y is the final exam score and x is the score on the first test. Brenda scored 95 on the first test. What is the predicted value of her score on the final exam?
90
85.5
none
95
95.5
In the course described above, Carlos scored a 90 on the first test and a 93 on the final exam. What is the value of his residual?
(a) –2.0 (b) 2.0 (c) 3.0 (d) 93 (e) none of these
2.0
None
3.0
-2.0
93
All but one of the following statements contains an error. Which statement could be correct?
We found a high correlation between the height and age of children: r = 1.12.
The correlation between mid-August soil moisture and the per-acre yield of tomatoes is r = 0.53.
We found a correlation of r = –0.63 between gender and political party preference.
The correlation between the distance travelled by a hiker and the time spent hiking is r = 0.9 meters per second.
There is a correlation of 0.54 between the position a football player plays and his weight.
What does the residual plot tell you about the linear model?
A residual plot is not an appropriate means for evaluating a linear model.
The curved pattern in the residual plot suggests that the linear model is not appropriate.
The linear model is appropriate, because there are approximately the same number of points above and below the horizontal line in the residual plot.
There are not enough data points to draw any conclusions from the residual plot.
The curved pattern in the residual plot suggests that there is no association between the weight and height of basketball players.
Which of the following is correct?
None is correct.
The predicted yield is 4.3 kg when the UV value is 20 Dobson units.
If the UV value increases by 1 Dobson unit, the yield is expected to increase by 0.0463 kg.
If the UV value increases by 1 Dobson unit, the yield is expected to decrease by 0.0463 kg.
If the yield increases by 1 kg, the UV value is expected to decrease by 0.0463 Dobson units.
Which statements below about least-squares regression are correct?
I. Switching the explanatory and response variables will not change the least-squares regression line.
II. The slope of the line is very sensitive to outliers with large residuals.
III. A value of r2 close to 1 does NOT guarantee that the relationship between the variables is linear.
Only I is correct
Only II is correct
Only III is correct
Both II and III are correct.
All three statements—I, II, and III—are correct.
An agricultural economist says that the correlation between corn prices and soybean prices is r = 0.7. This means that
the economist is confused, because correlation makes no sense in this situation.
when corn prices are above average, soybean prices tend to be below average.
when corn prices are above average, soybean prices also tend to be above average.
there is almost no relation between corn prices and soybean prices.
when soybean prices go up by 1 dollar, corn prices go up by 70 cents.
A copy machine dealer has data on the number of copy machines x at each of 89 customer locations and the number of service calls in a month y at each location. Summary calculations are given below. What is the slope of the least-squares regression line of number of service calls on number of copiers?
cannot be determine with the given information
0.48
2.82
0.86
1.56
In the setting of the previous problem, about what percent of the variation in the number of service calls is explained by the linear relation between number of service calls and number of machines?
