Consider the multiple regression modelYi = ẞ1 + ẞ2xi1 + … ….+ ẞkxik + Eiwhere the Ę;'s are independent and identically distributed as N(0, 0²) for i = 1, . . ., n, andk is the number of parameters.1. Show that an equivalent form of the usual F-test for testing the significance of theregression can be based on R² (squared multiple correlation coefficient) as follows:To test Hoẞ₂ = ẞ3 = = ßk = 0 versus H₁: at least one ß; ‡ 0, calculate=...=R² (n-k)Fo-(k − 1)(1 − R²)and reject Ho if the computed value of Fo exceeds Faa,k,n-k.2. Suppose a linear regression model as in part (1) with two regressors has been fittedto n = 25 observations and that R² = 0.90. Test for the significance of theregression at a = 0.05.

In multiple regression analysis, we often want to determine if the explanatory variables…

Answered: Consider the multiple regression model…

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter4: Writing Linear Equations

Section: Chapter Questions

Problem 12CR

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For 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 accuracy
The slope of a regression line (y on x) is -0.24, we know that SDy=3.2 and SDx=4.0, then the correlation coefficient between the two variables is:A. 0.3B. -0.3C. 0.8D. -0.8
One set of 20 pairs of scores, X and Y values, produces a correlation of r = 0.70. If SSY = 150, calculate the standard error of the estimate for the regression line
A set of n = 25 pairs of X and Y values has a correlation of r = -0.50 with SSX = 38 and SSY = 14. Find the standard error of estimate for the regression equation. What percentage of the variance in Y is accounted for by X?
One set of 10 pairs of scores, X and Y values produces a correlation of r= 0.40. If SSy = 200, find the standard of error of estimate for the regression line. You will need to calculate the SS residual first.
A trucking company considered a multiple regression model for relating the dependent variable y = total daily travel time for one of its drivers (hours) to the predictors x, = distance traveled (miles) and x, = the number of deliveries made. Suppose that the model equation is Y = -0.800 + 0.060x, + 0.900x2 + € (a) What is the mean value of travel time when distance traveled is 50 miles and four deliveries are made? 5.8 v hr (b) How would you interpret ß1 = 0.060, the coefficient of the predictor X1? o When the number of deliveries is held fixed, the average change in travel time associated with a one-mile (i.e. one unit) increase in distance traveled is 0.060 hours. O The total daily travel time increases by 0.060 hours when the distance traveled increases by 1. O When the number of deliveries is constant, the average change in travel time associated with a ten-mile (i.e. one unit) increase in distance traveled is 0.060 hours. O The average change in travel time associated with a…
a. Show that the regression R2 in the regression of Y on X is the squaredvalue of the sample correlation between X and Y. That is, show thatR2 = r2XY.b. Show that the R2 from the regression of Y on X is the same as the R2from the regression of X on Y. c. Show that ^β1 = rXY (sY/sX), where rXY is the sample correlationbetween X and Y, and sX and sY are the sample standard deviationsof X and Y.
Cou run a regression analysis on a bivariate set of data (n = obtain the regression equation 39). With 24.8 and = 43.4, you y = 2.058z - 27.113 with a correlation coefficient of r = 0.251. You want to predict what value (on average) for the response variable will be obtained from a value of 180 as the explanatory variable. What is the predicted response value? y = 343.3 (Report answer accurate to one decimal place.)
None
A trucking company considered a multiple regression model for relating the dependent variable y = total daily travel time for one of its drivers (hours) to the predictors x₁ = distance traveled (miles) and x₂ = the number of deliveries made. Suppose that the model equation is Y = -0.800+ 0.060x₁ +0.900x₂ + e (a) What is the mean value of travel time when distance traveled is 50 miles and four deliveries are made? hr (b) How would you interpret ₁ = 0.060, the coefficient of the predictor x₁? O When the number of deliveries is constant, the average change in travel time associated with a ten-mile (i.e. one unit) increase in distance traveled is 0.060 hours. O The total daily travel time increases by 0.060 hours when the distance traveled increases by 1. O When the number of deliveries is held fixed, the average change in travel time associated with a one-mile (i.e. one unit) increase in distance traveled is 0.060 hours. O The average change in travel time associated with a one-mile (i.e.…
*Based on the regression results, answer the following questions* A sample of data is collected (from 1999 and 2000) concerning the compensation of the executives (compensation is measured in 1000’s of $’s) of a number of public companies along with other firm-specific data. The dependent variable is total compensation, CEOANN is a dummy variable =1 for an individual who is a CEO and =0 for individuals who are not CEOs, EMPL is total employees, MKTVAL is the natural logarithm of the market value of the firm, EPSIN is earnings per share, YEAR is a dummy variable = 1 for the year 2000 and =0 for the year 1999, and ASSETS is the natural logarithm of the total assets of the company. Based on the regression results, answer the following questions e) Are any of the explanatory (independent) variables significant at the 10% level of significance? How do you know? f) What is the null and alternative hypothesis that Excel is testing in reporting the tstats above? g) What is the…
*Based on the regression results, answer the following questions* A sample of data is collected (from 1999 and 2000) concerning the compensation of the executives (compensation is measured in 1000’s of $’s) of a number of public companies along with other firm-specific data. The dependent variable is total compensation, CEOANN is a dummy variable =1 for an individual who is a CEO and =0 for individuals who are not CEOs, EMPL is total employees, MKTVAL is the natural logarithm of the market value of the firm, EPSIN is earnings per share, YEAR is a dummy variable = 1 for the year 2000 and =0 for the year 1999, and ASSETS is the natural logarithm of the total assets of the company. Based on the regression results, answer the following questions h) Is there a significant amount of evidence (say at the 10% level of significance) that CEO’s make at least $2 million more than non-CEO’s? i) Suppose you’re not sure if all the variables above should be included in the regression.…

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