3. A Ross MAP team is trying to estimate the revenues of major-league baseball teams during the regular season using a regression model. Currently, the independent variables include stadium capacity, the number of weekend games, the number of night games, and the number of Wins (out of 162 regular season games). One of your team members suggests that the model also should include the number of losses as it provides additional explanatory power. Assume that ties are not possible; so every game results in exactly one team winning and the other team losing. Which of the following statements is the most likely conclusion of the new regression model? (a) R2 will increase, adjusted R2 will decrease, and serror will decrease. (b) R2 and adjusted R2 will increase, and serror will decrease. (c) R2, adjusted R2, and serror will increase. (d) We cannot trust the regression output as some variables are highly correlated, resulting in multicollinearity.

3. A Ross MAP team is trying to estimate the revenues of major-league baseball teams during the regular season using a regression model. Currently, the independent variables include stadium capacity, the number of weekend games, the number of night games, and the number of Wins (out of 162 regular season games). One of your team members suggests that the model also should include the number of losses as it provides additional explanatory power. Assume that ties are not possible; so every game results in exactly one team winning and the other team losing. Which of the following statements is the most likely conclusion of the new regression model? (a) R2 will increase, adjusted R2 will decrease, and serror will decrease. (b) R2 and adjusted R2 will increase, and serror will decrease. (c) R2, adjusted R2, and serror will increase. (d) We cannot trust the regression output as some variables are highly correlated, resulting in multicollinearity.

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section: Chapter Questions

Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...

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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?
1. Suppose you wanted to predict Winnings ($) using only the number of poles won (Poles), the number of wins (Wins), the number of top five finishes (Top 5), or the number of top ten finishes (Top 10). Which of these four variables provides the best single predictor of winnings?2. Develop an estimated regression equation that can be used to predict Winnings ($) given the number of poles won (Poles), the number of wins (Wins), the number of top five finishes (Top 5), and the number of top ten (Top 10) finishes. Test for individual significance and discuss your findings and conclusions.3. Create two new independent variables: Top 2–5 and Top 6–10. Top 2–5 represents the number of times the driver finished between second and fifth place and Top 6–10 represents the number of times the driver finished between sixth and tenth place. Develop an estimated regression equation that can be used to predict Winnings ($) using Poles, Wins, Top 2–5, and Top 6–10. Test for individual significance and…
8)Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 11 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.86, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 86000 and the sum of squared errors (SSE) is 14000. From this information, what is MSE/MST? .5000 NONE OF THE OTHERS .2000 .3000 .4000
24) If the R-square value for a simple linear regression model is 0.80 and the regression line has anegative slope, the correlation coefficient describing the relationship between the two variables is_____________.
If the point representing 64 wins and attendance of 40,786, people per game is removed from the set of data and a new regression analysis is conducted, how would the following be mpacted?
The following results are from data concerning the amount withdrawn from an ATM machine based on the amount of time spent at the ATM machine (SECONDS) and the gender, FEMALE (dummy variable = 1 for females and = 0 for males) and an interaction term, SECONDS*FEMALE Based on the regression results, if a male and female each spend the same amount of time at the ATM machine (say 27 seconds), how much more (or less) will a male withdraw? (if a male withdraws more then your answer should be a positive number and if a male withdraws less then your answer should be a negative number? (please express your answer using 1 decimal places)
17) Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 41 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.9, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 90000 and the sum of squared errors (SSE) is 10000. From this information, what is the number of degrees of freedom for the t-distribution used to compute critical values for hypothesis tests and confidence intervals for the individual…
Given the estimated least square regression line y=2.48+1.63x, and the coefficient of determination of 0.81, What is the value of correlation coefficient?
(1) For neighborhoods with more than 66% of schools participating in free school lunch program, the estimated regression model is: crime_rate = 142.5737 - 1.9215(Prop_change_income) - 38.8741(0) - 19.20521(0) = 142.5737 - 1.9215(Prop_change_income) (2) For neighborhoods with 33% to 66% of schools participating in free school lunch program, the estimated regression model is: crime_rate = 142.5737 - 1.9215(Prop_change_income) - 38.8741(0) - 19.20521(1) = 123.36849 - 1.9215(Prop_change_income) (3) For neighborhoods with less than 33% of schools participating in free school lunch program, the estimated regression model is: crime_rate = 142.5737 - 1.9215(Prop_change_income) - 38.8741(1) - 19.20521(0) = 103.69959 - 1.9215(Prop_change_income) Questions: 1. What is difference between models in 1,2,and 3? 2. Which estimated model 1,2, or 3 results in the line with the highest estimated crime rates (the highest positioned line)?
(1) For neighborhoods with more than 66% of schools participating in free school lunch program, the estimated regression model is: crime_rate = 142.5737 - 1.9215(Prop_change_income) - 38.8741(0) - 19.20521(0) = 142.5737 - 1.9215(Prop_change_income) (2) For neighborhoods with 33% to 66% of schools participating in free school lunch program, the estimated regression model is: crime_rate = 142.5737 - 1.9215(Prop_change_income) - 38.8741(0) - 19.20521(1) = 123.36849 - 1.9215(Prop_change_income) (3) For neighborhoods with less than 33% of schools participating in free school lunch program, the estimated regression model is: crime_rate = 142.5737 - 1.9215(Prop_change_income) - 38.8741(1) - 19.20521(0) = 103.69959 - 1.9215(Prop_change_income) Questions: 1. What is difference between models in 1,2,and 3? 2. Which estimated model 1,2, or 3 results in the line with the highest estimated crime rates (the highest positioned line)? 3. Test whether the crime rate in neighborhoods with 33% to 66% of…
Mr. James, president of Daniel-James Financial Services, believes that there is a relationship between the number of client contacts and the dollar amount of sales. To document this assertion, he gathered the following information from a sample of clients for the last month. Let X represent the number of times that the client was contacted and Y represent the valye of sales ($1000) for each client sampled. Number of Contacts (X) Sales ($1000) 14 24 12 14 20 28 16 30 23 30 a) Compute the regression equation for client contacts and sales. Interpret the slope and intercept parameters.
Suppose that a least squares regression line equation is ˆy = 1.65 − 2.20x and the actual y value corresponding to x = 10 is −19, what is the residual value corresponding to y = −19?