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 tasked with studying the effect of class size on test scores for high school students. You collect data on class size and test
scores from 100 high school classes. You then run an OLS regression of test scores on class size. The results for the intercept and slope
coefficient on class size are 520.4 and -5.82, respectively with an R-Squared of 0.08. If a class goes from a class size of 19 students to a class
size of 23 students, what do these results predict will be the change in test scores?
102.54
a.
b.23.28
28.65
C.
None of these
d.
19.89
e.
Which of the following is NOT a plot of residuals typically used in multiple regression analysis with two independent variables (X1 and X2)?
Select one:
a.
Residuals versus X2.
b.
Residuals versus correlation coefficients.
c.
Residuals versus time.
d.
Residuals versus X1.
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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_forwardTable 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_forward
- Table 2 shows a recent graduate’s credit card balance each month after graduation. a. Use exponential regression to fit a model to these data. b. If spending continues at this rate, what will the graduate’s credit card debt be one year after graduating?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_forwardFor the following exercises, consider the data in Table 5, which shows the percent of unemployed in a city ofpeople25 years or older who are college graduates is given below, by year. 41. Based on the set of data given in Table 7, calculatethe regression line using a calculator or othertechnology tool, and determine the correlationcoefficient to three decimal places.arrow_forward
- For the following exercises, consider the data in Table 5, which shows the percent of unemployed ina city of people 25 years or older who are college graduates is given below, by year. 40. Based on the set of data given in Table 6, calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient to three decimal places.arrow_forwardStoaches are fictional creatures that nest in truffula forests. A researcher wants to know whether there is a relationship between a stoach’s wingspan (?W, the predictor) and its nest height (?H, the response). A sample of 88 stoaches is observed, and for each, the wing-span (in cm) and the nest height (in m) are recorded. The observed data meet the assumptions for a linear regression, so the researcher fits the regression model and obtains a regression equation ℎ̂=−0.813+0.177?,h^=−0.813+0.177w, with standard error for the coefficient of ?w equal to 0.448. Determine the ?p-value from a test for a statistically significant linear dependence of nest height on wing-span. (Give your answer to 4 decimal places.arrow_forwardSuppose we fit a regression line to predict the number of incidents of skin cancer per 1,000 people from the number of sunny days in a year. For a particular year, we predict the incidence of skin cancer to be 1.5 per 1,000 people, and the residual for this year is 0.5. Did we over or under estimate the incidence of skin cancer? Explain your reasoning.arrow_forward
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