Pearson eText Business Statistics: First Course -- Instant Access (Pearson+)
8th Edition
ISBN: 9780136880974
Author: David Levine, David Stephan
Publisher: PEARSON+
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Suppose the athletic director at a university would like to develop a regression model to predict the point differential for games played by the men's basketball team. A point differential is the difference between the final points scored by two competing teams. A positive differential is a win, and a negative differential is a loss. For a random sample of games, the point differential was calculated, along with the number of assists, rebounds, turnovers, and personal fouls. Use the data in the accompanying table attached below to complete parts a through e below. Assume a = 0.05.
a) Using technology, construct a regression model using all three independent variables.
y = __ + (_)x1 + (_)x2 + (_)x3 + (_)x4
b) Test the significance of each independent variable using a= 0.10.
c) interpret the p-value for each independent variable.
d) Construxt a 90% confidence interval for the regression coefficients for each independent variable and interpret the meaning.
e) Using the results from…
Suppose you are examining a multi-variable linear regression model that was designed to predict the weight of a person, measured in kg, using 3 predictor variables. One of the variables used in this analysis is "height", with the coefficient of this variable being equal to 3.96, with a standard error of the coefficient equal to 1.168. There are 300 datapoints in the dataset. Using this information, what would be the test statistic (t-ratio) for the test to see if the variable "height" is significant?
Only round final answer. Round to two decimal places.
A local retail store compared their monthly sales of umbrellas with the amount of rainfall that occured
during that month. They computed the following statistics:
Rainfall (in) # of umbrellas
mean = 4.64
mean = 34.2
SD = 1.17
SD = 13.2
r = 0.8
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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_forwardFor the following exercises, use Table 4 which shows the percent of unemployed persons 25 years or older who are college graduates in a particular city, by year. Based on the set of data given in Table 5, calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient. Round to three decimal places of accuracyarrow_forward
- Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to 2012. a. Let x represent time in years starting with x=0 for the year 1997. Let y represent the number of seals in thousands. Use logistic regression to fit a model to these data. b. Use the model to predict the seal population for the year 2020. c. To the nearest whole number, what is the limiting value of this model?arrow_forwardListed below are systolic blood pressure measurements (in mm Hg) obtained from the same woman. Find the regression equation, letting the right arm blood pressure be the predictor (x) variable. Find the best predicted systolic blood pressure in the left arm given that the systolic blood pressure in the right arm is 90 mm Hg. Use a significance level of 0.05 Right arm - 102; 101; 94; 79; 80 Left arm - 177; 172; 143; 144; 143 The regression equation is y(carety)= ___+___x. Given that the systolic blood pressure in the right arm is 90mm Hg, the best predicted systolic blood pressure in the left arm is _____ mm Hg.arrow_forwardAccountants at the Renong and Khalid Accountant Company believed that several traveling executives were submitting unusually high travel vouchers when they returned from business trips. First, they took a sample of 200 vouchers submitted from the past year. Then they developed the following multiple-regression equation relating expected travel cost (Y) to number of days on the road (X1) and distance travelled (X2) in miles: Y = 90.00 + 48.50X1 + 0.40X2 Here is additional information concerning the regression model: Sb1 = 0.038 Sb2 =0.019 R? = 0.68 Se = 1.63 F-Statistic = 32.123 Durbin-Watson (d) statistic = 0.5436 a) Which of the independent variables appear to be statistically significant (at the 0.05 significant level) in explaining the expected travel cost for accountants? Explain. b) (Mr. Ghazali returns from a 200-mile trip that took him out of town for 5 days), what is the expected amount of his claim. c) What proportion of the total variation in expected travel cost is explained…arrow_forward
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