STATISTICS F/BUSINESS+ECONOMICS-TEXT
13th Edition
ISBN: 9781305881884
Author: Anderson
Publisher: CENGAGE L
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Textbook Question
Chapter 14.8, Problem 45E
Given are data for two variables, x and y.
| xi | 6 | 11 | 15 | 18 | 20 |
| yi | 6 | 8 | 12 | 20 | 30 |
- a. Develop an estimated regression equation for these data.
- b. Compute the residuals.
- c. Develop a plot of the residuals against the independent variable x. Do the assumptions about the error terms seem to be satisfied?
- d. Compute the standardized residuals.
- e. Develop a plot of the standardized residuals against y. What conclusions can you draw from this plot?
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Given are five observations for two variables, x and y.
xi
3
12
6
20
14
yi
55
45
50
15
20
#1) Develop the estimated regression equation by computing the values of b0 and b1 using
b1 =
Σ(xi − x)(yi − y)
Σ(xi − x)2
and
b0 = y − b1x.
y=
#2) Use the estimated regression equation to predict the value of y when x = 13.
Given are five observations for two variables, x and y.
xi
1
2
3
4
5
yi
4
6
6
11
13
Develop the estimated regression equation by computing the values of
b0
and
b1
using
b1 =
Σ(xi − x)(yi − y)
Σ(xi − x)2
and
b0 = y − b1x.
ŷ =
(e)
Use the estimated regression equation to predict the value of y when
x = 2.
Given are five observations for two variables, x and y.xi -3 12 6 20 14yi -55 40 55 10 15 Develop the estimated regression equation by computing the values of
b0 and b1 using b1 =
Σ(xi − x)(yi − y)
Σ(xi − x)2
and
b0 = y − b1x.
y= ____________________
Use the estimated regression equation to predict the value of y when x = 7.
_____________________________
Chapter 14 Solutions
STATISTICS F/BUSINESS+ECONOMICS-TEXT
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- Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?arrow_forwardGiven are data for two variables, x and y. xi 6 11 15 18 20 yi 5 9 13 19 30 An estimated regression equation for these data is yhat=-7.24+1.6x a) Compute the residuals. (Round your answers to two decimal places.) b) Compute the standardized residuals. (Round your answers to two decimal places.) Ans both..otherwise don't answerarrow_forwardGiven are five observations for two variables, x and y. xi 1 2 3 4 5 yi 4 6 5 9 14 Develop the estimated regression equation by computing the the slope and the y intercept of the estimated regression line (to 1 decimal). y^= + x Use the estimated regression equation to predict the value of y when x = 5 (to 1 decimal).y^ =arrow_forward
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