Consider the multiple regression model shown next between the dependent variable Y and four independent variables X1, X2, X3, and X4, which results in the following function: Ŷ = 33 + 8X1 − 6X2 + 16X3 + 18X4 For this model, there were 43 observations; SSR = 1,464 and SSE = 600. The critical F-value at the 1% level of significance is Multiple Choice 3.94 2.72 3.86 2.64

Consider the multiple regression model shown next between the dependent variable Y and four independent variables X1, X2, X3, and X4, which results in the following function: Ŷ = 33 + 8X1 − 6X2 + 16X3 + 18X4 For this model, there were 43 observations; SSR = 1,464 and SSE = 600. The critical F-value at the 1% level of significance is Multiple Choice 3.94 2.72 3.86 2.64

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter4: Linear Functions

Section: Chapter Questions

Problem 30PT: For the following exercises, use Table 4 which shows the percent of unemployed persons 25 years or...

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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
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?
Consider the multiple regression model shown next between the dependent variable Y and four independent variables X1, X2, X3, and X4, which results in the following function:Ŷ = 33 + 8X1 − 6X2 + 16X3 + 18X4For this model, there were 35 observations; SSR = 1,544 and SSE = 600. Assume a 0.01 significance level.Based on the given information, which of the following conclusions is correct about the statistical significance of the overall model? Multiple Choice Reject the null hypothesis that β3 = 0. Do not reject the null hypothesis that β1 = β2 = β3 = β4 = 0. Reject the null hypothesis that β1 = 0. Reject the null hypothesis that β1 = β2 = β3 = β4 = 0.
Which of the multivariate regression parameters listed below would be best interpreted as: the predicted value on the dependent variable when all of the independent variables in the model are equal to zero. a b1 X1 R2
A researcher would like to predict the dependent variable YY from the two independent variables X1X1 and X2X2for a sample of N=20N=20 subjects. Use multiple linear regression to calculate the coefficient of multiple determination and test the significance of the overall regression model. Use a significance level α=0.02. X1X1 X2X2 YY 31.4 32.3 25.2 85.4 28.1 53 66.3 42.6 67.4 59 56.1 70.7 52.4 40.4 39.7 86.4 23.7 35 50.9 36.7 34.4 74.4 38 64.9 57.3 47.6 67.4 61.9 33.3 41.3 48.6 49.7 53.6 46.6 47.2 34.5 31.8 38.7 40.9 86 55 74 69.8 27.7 45.9 65.8 48.2 42.4 44.7 55.3 55.1 57.3 27 31.5 60.4 28.1 19.4 65.9 26 13.7 SSreg= SSres= R2= F= P-value = What is your decision for the hypothesis test? Reject the null hypothesis, H0:β1=β2=0 Fail to reject H0H0 What is your final conclusion? The evidence supports the claim that one or more of the regression coefficients is non-zero The evidence supports the claim that all of the regression…
A researcher would like to predict the dependent variable YY from the two independent variables X1X1 and X2X2 for a sample of N=20N=20 subjects. Use multiple linear regression to calculate the coefficient of multiple determination and test the significance of the overall regression model. Use a significance level α=0.05α=0.05. X1X1 X2X2 YY 65.4 65.8 57.3 72.8 70.8 55.1 63.3 59.9 66.9 59.1 60.4 60.4 65.4 66.9 56.2 58.3 61.9 50.4 57.1 57.1 54.2 78.2 62.5 67.5 54.2 55.9 57.1 56.5 55.5 57.8 57.9 56.2 60.8 54.3 54.8 61.8 68.2 70.5 71.8 60 64.1 58.8 66.6 60.5 54.6 66.7 68.5 51.7 45.1 48.6 57.1 58.4 59.9 55.9 58.6 66.3 52.5 56 60.5 67.1 SSreg=SSres=R2=F=P-value =
Given the partial results from a linear regression model below, a sample size of 504, and ɑ=0.05, What is the F-Statistic for the overall model? Is it statistically significant? What is the R2 for the regression model above?
A researcher would like to predict the dependent variable YY from the two independent variables X1X1 and X2X2 for a sample of N=10N=10 subjects. Use multiple linear regression to calculate the coefficient of multiple determination and test statistics to assess the significance of the regression model and partial slopes. Use a significance level α=0.01α=0.01. X1X1 X2X2 YY 58.8 29.9 63.1 64.1 57.3 40.1 51.4 35.3 46.2 77.1 88.5 30 60.6 67.5 16.2 68.3 63.4 62 44.8 6.6 77.6 49 29.3 65.5 55.5 25.8 62.5 57.5 30.2 62 R2=R2= F=F= P-value for overall model = t1=t1= for b1b1, P-value = t2=t2= for b2b2, P-value = What is your conclusion for the overall regression model (also called the omnibus test)? The overall regression model is statistically significant at α=0.01α=0.01. The overall regression model is not statistically significant at α=0.01α=0.01. Which of the regression coefficients are statistically different from zero? neither regression coefficient is…
A researcher would like to predict the dependent variable YY from the two independent variables X1X1 and X2X2for a sample of N=13N=13 subjects. Use multiple linear regression to calculate the coefficient of multiple determination and test statistics to assess the significance of the regression model and partial slopes. Use a significance level α=0.02α=0.02. X1X1 X2X2 YY 40.6 66.7 59 27.2 72.4 42.3 65 56.2 69.1 17.3 71.2 25.4 30 65.6 40.9 41.2 59.1 44.8 68.5 44.3 40.6 79.5 37.3 54.7 55.6 58 66.3 59.4 46.1 27.2 62.9 42.4 30.9 67.2 44.5 39.5 22.6 64.3 18.4 R2= F= P-value for overall model = t1= for b1, P-value = t2= for b2, P-value = What is your conclusion for the overall regression model (also called the omnibus test)? The overall regression model is statistically significant at α=0.02. The overall regression model is not statistically significant at α=0.02. Which of the regression coefficients are statistically different from zero? neither…
researcher would like to predict the dependent variable YY from the two independent variables X1X1 and X2X2 for a sample of N=20N=20 subjects. Use multiple linear regression to calculate the coefficient of multiple determination and test the significance of the overall regression model. Use a significance level α=0.05α=0.05. X1X1 X2X2 YY 33.2 35.8 45.7 25.1 47.7 41.9 86.6 54.4 89.5 55.8 51.3 76.8 65.8 60.5 40.9 26.9 50.1 44.7 67.5 58.1 61.7 35.9 61.9 20 48.8 44.8 52.8 47.9 42.7 44.9 43.4 56.6 15.4 50.9 43.7 53.9 51.3 46 79.8 39.8 55.1 56 33 56.1 30.6 45.9 55 47.6 19.4 50.9 40.4 74.7 45.8 84.6 62.3 58.9 86.5 64.2 64.1 49.2 SSreg=SSreg= SSres=SSres= R2=R2= F=F= P-value = What is your decision for the hypothesis test? Reject the null hypothesis, H0:β1=β2=0H0:β1=β2=0 Fail to reject H0H0 What is your final conclusion? The evidence supports the claim that one or more of the regression coefficients is non-zero The evidence supports the…
A researcher would like to predict the dependent variable YY from the two independent variables X1X1 and X2X2 for a sample of N=11N=11 subjects. Use multiple linear regression to calculate the coefficient of multiple determination and test statistics to assess the significance of the regression model and partial slopes. Use a significance level α=0.05α=0.05. X1X1 X2X2 YY 52.3 45.6 49.1 55.9 48.7 53.1 46.5 47.4 45.9 52 45.6 59.8 48.9 45.5 52.6 46.2 35.1 71.2 28.8 32.6 33.5 40.7 41 40.3 43.7 40 65.8 47 37.8 52.8 34.2 28 53.5 R2=R2= (Not the adjusted R2R2) FF test statistic = P-value for overall model = test statistic for b1b1 p-value for the two-tailed test = test statistic for b2b2 p-value for the two-tailed test = What is your conclusion for the overall regression model at the 0.05 alpha level (also called the omnibus test)? The overall regression model is statistically significant at α=0.05α=0.05. The overall…
Which of the multivariate regression parameters listed below would be best interpreted as: the proportion of variation in the dependent variable explain by all the independent variables in the model. a b1 X1 R2