Introduction To Statistics And Data Analysis
6th Edition
ISBN: 9781337793612
Author: PECK, Roxy.
Publisher: Cengage Learning,
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Chapter 13, Problem 62CR
a.
To determine
Estimate the population regression line.
b.
To determine
Compute the estimated standard deviation,
Conduct a test to check whether the y intercept of the population regression line differs from zero.
c.
To determine
Compute the 95% confidence interval for
Check whether the result indicates that
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For a given set of x and y data values, assume that the regression model assumptions are valid and that a 90% confidence interval for ₁ is given by (-2.2, -0.1).
Which of the following statements are true?
i) At a = 0.10, there is a significant linear relationship between x and y.
ii) In the scatterplot of x and y, the values of y tend to decrease as the values of x increase.
iii) Based on this confidence interval, we would reject the null hypothesis of no linear relationship at any significance level a ≤ 0.1.
Select one:
a. i)
O b. i) and ii)
O c. ii)
d. i), ii), and iii)
In simple linear regression, at what value of the independent variable, X, will the 95% confidence interval for the average value of Y be narrowest? At what value will the 95% prediction interval for the value of Y for a sin gle new observation be narrowest?
A regression model to predict Y, the state burglary rate per 100,000 people for 2005, used the following four state predictors: X1 = median age in 2005, X2 = number of 2005 bankruptcies, X3 = 2004 federal expenditures per capita (a leading predictor), and X4 = 2005 high school graduation percentage. (a) Fill in the values in the table given here for a two-tailed test at α = 0.01 with 40 d.f. (Negative values should be indicated by a minus sign. Leave no cells blank - be certain to enter "0" wherever required. Round your t-values to 3 decimal places and p-values to 4 decimal places.)
Predictor
Coefficient
SE
tcalc
p-value
Intercept
4,641.0430
798.0634
AgeMed
-28.863
12.4684
Bankrupt
20.1604
12.1079
FedSpend
-0.0181
0.0181
HSGrad%
-30.3196
7.1136
(b-1) What is the critical value of Student's t in Appendix D for a two-tailed test at α = .01 with 40 d.f? (Round your answer to 3 decimal places.) t-value = (b-2) Choose the correct option.…
Chapter 13 Solutions
Introduction To Statistics And Data Analysis
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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_forwardWhat does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?arrow_forwardFind the equation of the regression line for the following data set. x 1 2 3 y 0 3 4arrow_forward
- A regression model to predict Y, the state burglary rate per 100,000 people for 2005, used the following four state predictors: X1 = median age in 2005, X2 = number of 2005 bankruptcies, X3 = 2004 federal expenditures per capita (a leading predictor), and X4 = 2005 high school graduation percentage. (a) Fill in the values in the table given here for a two-tailed test at α = 0.01 with 35 d.f. (Negative values should be indicated by a minus sign. Leave no cells blank - be certain to enter "0" wherever required. Round your t-values to 3 decimal places and p-values to 4 decimal places.) Predictor Coefficient SE tcalc p-value Intercept 4,286.0597 795.8817 AgeMed -26.986 12.0335 Bankrupt 18.5775 12.9258 FedSpend -0.0153 0.0150 HSGrad% -28.5624 7.1571 (b-1) What is the critical value of Student's t in Appendix D for a two-tailed test at α = .01 with 35 d.f? (Round your answer to 3 decimal places.) t-value =arrow_forwardSuppose we perform a simple linear regression (SLR) of two variables F1 and F2 against the same out variable (say y). The r-squared value/score of both the SLRS are 0.9678 and 0.95123 respectively for F1 and F2. Then what can you say about the correlation? O a. y is more dependent on F2 than F1 O b. None of these O . The result does not say that y is more dependent on F1 OR F2 O d.y is more dependent on F1 than F2arrow_forwardA regression model to predict Y, the state burglary rate per 100,000 people for 2005, used the following four state predictors: X1 = median age in 2005, X2 = number of 2005 bankruptcies, X3 = 2004 federal expenditures per capita (a leading predictor), and X4 = 2005 high school graduation percentage. (a) Fill in the values in the table given here for a two-tailed test at α = 0.01 with 33 d.f. (Negative values should be indicated by a minus sign. Leave no cells blank - be certain to enter "0" wherever required. Round your t-values to 3 decimal places and p-values to 4 decimal places.) Predictor Coefficient SE tcalc p-value Intercept 4,579.5465 791.5050 AgeMed -27.292 12.1893 Bankrupt 19.5612 12.0754 FedSpend -0.0132 0.0116 HSGrad% -27.5839 7.1731 (b-1) What is the critical value of Student's t in Appendix D for a two-tailed test at α = .01 with 33 d.f? (Round your answer to 3 decimal places.) t-value = (b-2) Choose the correct option.…arrow_forward
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