Exercise 5 Answer the following questions: a. You are given below the regression of y on 4 predictors. q <- lm(y ~ x1+x2+x3+x4) summary(q) Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 13.56711 4.48937 3.022 0.002693 ** x1 -10.57675 1.91288 -5.529 6.26e-08 *** x2 -1.34335 0.39868 -3.370 0.000836 *** x3 1.03066 0.05588 18.445 < 2e-16 *** x4 -0.30955 0.16017 -1.933 0.054088 . Signif. codes: 0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1 Residual standard error: 22.85 on 354 degrees of freedom Multiple R-squared: 0.5286, Adjusted R-squared: 0.5233 F-statistic: 99.26 on 4 and 354 DF, p-value: < 2.2e-16 Compute the partial coefficient of determination (squared of the partial correlation coefficient) of y with $x_1$ given the other three variables are in the model.
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We are given the multiple regression model: $\ln(y) = 13.56711 - 10.57675x_1 - 1.34335x_2 + 1.03066x_3 - 0.30955x_4$. Show more…
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Look at the following output from a linear regression in R. What is the amount of variability in Y that is explained by the model? ## Call: ## lm(formula = y ~ x, data = my.data) ## ## Residuals: ## Min 1Q Median 3Q Max ## -29.069 -9.525 -2.272 9.215 43.201 ## ## Coefficients: ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) 42.9800 2.1750 19.761 < 2e-16 *** ## x 3.9324 0.4155 9.464 1.49e-12 *** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## Residual standard error: 15.38 on 48 degrees of freedom ## Multiple R-squared: 0.6511, Adjusted R-squared: 0.6438 ## F-statistic: 89.57 on 1 and 48 DF, p-value: 1.49e-12 About 89.6%, using the F statistic 3.93%, using the coefficient for the variable X There is no information on this output for me to answer the question. About 64%, using the adjusted R-squared
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Question 9: Use the following regression results to answer the question below: Regression Statistics Multiple R 0.8851 R Square 0.7835 Adjusted R Square 0.7474 Standard Error 5.4006 Observations 8 ANOVA df SS MS F Regression 1 633.242 633.242 21.711 Residual 6 175.000 29.167 Total 7 808.242 Coefficients Standard Error t Stat P-value Intercept 5.93118 4.17721 1.41989 0.20545 Total Bill -2.71551 0.58279 -4.65952 0.00347 Which of the following is true? The correlation between x and y must be approximately -0.7835. The correlation between x and y must be approximately 0.8851. The correlation between x and y must be approximately -0.8851. The correlation between x and y must be approximately 0.7835.
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