EBK BUSINESS STATISTICS
7th Edition
ISBN: 9780134462783
Author: STEPHAN
Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)
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One of the residuals in a linear regression model is equal to 6.5. Other results from the model areMSE = 3.2, MSR = 4.5, SSE = 182, and SSR = 243. The value of the standardized residual is:a. 3.06b. 3.63c. 0.48d. 0.42e. None of the other answers is correct
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.
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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_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 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_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 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_forwardAn engineer performed an experiment to determine the effect of CO2 pres- sure, CO, temperature, peanut moisture, CO2 flow rate, and peanut particle size on the total yield of oil per batch of peanuts. Table B.7 summarizes the experimental results. e. Find a 95% CI for the regression coefficient for temperature for both models in part d. Discuss any differences.arrow_forwardCh 13. 7: Refer to the Lincolnville School District bus data. First, add a variable to change the type of engine (diesel or gasoline) to a qualitative variable. If the engine type is diesel, then set the qualitative variable to 0. If the engine type is gasoline, then set the qualitative variable to 1. Develop a regression equation using statistical software with maintenance cost as the dependent variable and age, odometer miles, miles since last maintenance, and engine type as the independent variables.arrow_forward
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- A researcher examined the problem of obesity among boys and girls. A random sample of six children gave the following data on age and body mass index. The distributions were assumed normal and the standard deviations equal. Age(in years) 4 6 8 11 14 16 Body Mass Index 18.1 16.8 20.6 21.5 23.8 24.5 Find the equation for the regression line. Is the y-intercept in this equation useful as a predictor of BMI? WHY OR WHY NOT? Interpret the slope in terms of this problem. Explain the meaning of the coefficient of determination in terms of this problem. If the age of a child is 9 years old, what body mass index would you predict for the child? IF NOT APPROPRIATE, WHY? If the age of a child is 6 years old, what body mass index would you predict for the child? IF NOT APPROPRIATE, WHY? What is the correlation coefficient for this problem? Do the data indicate a strong linear relationship between age and body mass…arrow_forwardConsider the SPSS regression output below. The dependent variable (Y) is the level of happiness felt by individuals. The dependent variable was measured in the following manner: 1= very unhappy, 2= somewhat unhappy, 3=neither unhappy nor happy, 4= somewhat happy, 5= very happy. The following four factors are the independent variables: highest year of school completed, respondent’s age, number of children of the respondent, and total family income. The researcher acquired data from 1,457 randomly selected Americans and ran a multiple regression. The regression results are presented below: Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .215a .046 .043 .72476 a. Predictors: (Constant), TOTAL FAMILY INCOME, AGE OF RESPONDENT, NUMBER OF CHILDREN, SUBJECTIVE CLASS IDENTIFICATION, HIGHEST YEAR OF SCHOOL COMPLETED Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig.…arrow_forwardA researcher conducted a number of descriptive statistics for two variables X and Y. They were as follows: SP = 15; SSx = 3; My = 7; Mx = 3 What is b equal to (Please include the sign: e.g., -20)? What is a equal to (please include the sign: e.g., +4.0)? Using b and a construct a regression equation, and then using the regression equation, calculate the value of predicted Y when X = 2?arrow_forward
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