EBK BUSINESS STATISTICS
8th Edition
ISBN: 9780135179833
Author: STEPHAN
Publisher: VST
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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…
2. The instructor of a mathematics class collected data to see whether there is a correlation
between the number of absences (X) and the student's score on the final exam (Y). The
number of absences and score on the final exam were recorded. The following regression
equation was obtained: Final score = 92.5317 – 3.7611 (Absences)
a) (5 points) What would be the predicted final exam score for a student that had 10
absences?
b) (5 points) The student from part (a) actually scored a 60 on the final exam. What is the
residual for this student? Show all work.
The higher the difference between the observed value of y and the predicted value
of y, the better the regression model is.
Select one:
O True
False
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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
- If a scatterplot is created in excel, and a line of regression is fit along with a derived functional form, what does it mean to describe and interpret them? What conclusions would be made about relationships between two recorded variables?arrow_forwardThe following equation is the result of performing a multiple regression analysis: Job performance = 10 + (5*job knowledge) + (0.7* conscientiousness), where job knowledge is measured on a scale of 0-5 and conscientiousness is measured on a scale of 0 to 100. Which of the following conclusions is correct? !! O If a person scored 5 on job knowledge and 100 on conscientiousness he or she would have the maximum predictive score possible If a person scored 0 on both job knowledge and conscientiousness, his or her predictive score is 0 ONeither job knowledge nor conscientiousness predicts performance O Conscientiousness is less important than job knowledge. Question 3! For a measuring tool to be usefulitmus bearrow_forward32)arrow_forward
- Suppose the following data were collected from a sample of 1515 CEOs relating annual salary to years of experience and the economic sector their company belongs to. Use statistical software to find the following regression equation: SALARYi=b0+b1EXPERIENCEi+b2SERVICEi+b3INDUSTRIALi+eiSALARY�=�0+�1EXPERIENCE�+�2SERVICE�+�3INDUSTRIAL�+��. Is there enough evidence to support the claim that on average, CEOs in the industrial sector have lower salaries than CEOs in the financial sector at the 0.050.05 level of significance? If yes, write the regression equation in the spaces provided with answers rounded to two decimal places. Else, select "There is not enough evidence." Copy Data CEO Salaries Salary Experience Service (1 if service sector, 0 otherwise) Industrial (1 if industrial sector, 0 otherwise) Financial (1 if financial sector, 0 otherwise) 141150141150 1010 11 00 00 176000176000 3232 11 00 00 139938139938 99 00 11 00 203577203577 3030 00 00 11 148032148032 22 00…arrow_forwardSuppose the following data were collected from a sample of 1515 CEOs relating annual salary to years of experience and the economic sector their company belongs to. Use statistical software to find the following regression equation: SALARYi=b0+b1EXPERIENCEi+b2SERVICEi+b3INDUSTRIALi+eiSALARY�=�0+�1EXPERIENCE�+�2SERVICE�+�3INDUSTRIAL�+��. Is there enough evidence to support the claim that on average, CEOs in the service sector have lower salaries than CEOs in the financial sector at the 0.010.01 level of significance? If yes, write the regression equation in the spaces provided with answers rounded to two decimal places. Else, select "There is not enough evidence." Copy Data CEO Salaries Salary Experience Service (1 if service sector, 0 otherwise) Industrial (1 if industrial sector, 0 otherwise) Financial (1 if financial sector, 0 otherwise) 144225144225 1010 11 00 00 187765187765 2020 00 00 11 142500142500 66 11 00 00 169650169650 2828 11 00 00 167250167250 3131 00…arrow_forward2. What is the use of the regression line? C. A student conducted a regression analysis between the math grades of his classmates and the number of times they were absent in the subject. He found that the regression line that will predict the grade (y) if the number of absences (x) is known =97.732 2.61x. ances? absences? 457 conces? 1533 ? 4. What is the predicted grade of a student who has 1 absence? 5. What is the predicted grade of a student who has 0 absences?arrow_forward
- If the R-squared for a regression model relating the outcome y to an explanatory variable x is 0.9. This implies that there is a positive linear relationship between y and x. Select one: True Falsearrow_forwardA set of X and Y scores has MX = 4, SSX = 10, MY = 5, SSY = 40, and SP = 20. Which is the regression equation for predicting Y from X?arrow_forwardTYPEWRITTEN ONLY FOR UPVOTE. DO THIS COMPLETELY. SHOW SOLUTIONS AND ALSO FILL OUT THE TABLE BELOW. SKIP IF YOU ALREADY DID THISarrow_forward
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