In a regression analysis involving 30 observations, the following estimated regression equation was obtained. ý= 17.6 +3.8x, -2.3x₂ +7.6x₂ +2.7% For this estimated regression equation, SST = 1,805 and SSR = 1,760. (a) At a = 0.05, test the significance of the relationship among the variables. State the null and alternative hypotheses. OH One or more of the parameters is not equal to zero. H₁₂₁ P₁ =B₁₂ =B₂ =B₁ = 0 OH: One or more of the parameters is not equal to zero. H₂: B₁ =B₁ =B₁₂ =B3 =B₁ = 0 1 2 OHB₁ =B₁ B₂ =B₁ =B₁ = 0 H: One or more of the parameters is not equal to zero. OH₁¹ B₁ =B₁₂=B₂ = P₁ = 0 H: One or more of the parameters is not equal to zero. Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value = State your conclusion. O Reject H. We conclude that the overall relationship is significant. O Do not reject H. We conclude that the overall relationship is not significant. O Do not reject H. We conclude that the overall relationship is significant. O Reject H We conclude that the overall relationship is not significant. Suppose variables x, and x, are dropped from the model and the following estimated regression equation is obtained. 11.13.6x₂ + 8.1x For this model, SST = 1,805 and SSR = 1,695. (b) Compute SSE(x₂x₂x₂x₂). SSE (X₁ X₂ X3 X4) (c) Compute SSE(x₂x₂). SSE(x₁, x₂) = (d) Use an F test and a 0.05 level of significance to determine whether x, and x, contribute significantly to the model. State the null and alternative hypotheses. OH: One or more of the parameters is not equal to zero. H₂1 P₁ =B₁ = 0 OH₁B₂₁ =B₁₂ = 0 H: One or more of the parameters is not equal to zero. OH: One or more of the parameters is not equal to zero. H₂: B₂ =B₂ = 0 OH₁: B₁ =B₁=0 H: One or more of the parameters is not equal to zero. Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value = State your conclusion. O Reject H. We conclude that x, and x, do not contribute significantly to the model. O Do not reject H. We conclude that x, and x, contribute significantly to the model. O Reject H. We conclude that x, and x, contribute significantly to the model. O Do not reject H. We conclude that x, and x, do not contribute significantly to the model.

The following regression model was fitted to sample data with 12 observations: = 30 +4.50x. What is the residual for an observation (x = 2, y = 40)? 0.50 -1 1 -0.50

The following estimated regression equation based on 10 observations was presented. ŷ= 29.1230+ 0.5806x + 0.4380x2 The values of SST and SSR are 6,725.125 and 6,223.375, respectively. (a) Find SSE. SSE= (b) Compute R2. (Round your answer to three decimal places.) R² = (c) Compute R. (Round your answer to three decimal places.) R2= (d) Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.) O The estimated regression equation did not provide a good fit as a large proportion of the variability in y has been explained by the estimated regression equation. O The estimated regression equation did not provide a good fit as a small proportion of the variability in y has been explained by the estimated regression equation. O The estimated regression equation provided a good fit as a large proportion of the variability in y has been explained by the estimated regression equation. O The estimated regression equation provided a good fit…

The arm span and foot length were both measured (in centimeters) for each of 20 students in a biology class. The computer output displays the regression analysis. Predictor Coef SE Coef t-ratio Constant Arm span -7.611 2.567 2.965 0.046 0.186 0.035 5.377 0.000 S = 1.61 R-Sq = 63.0% R-Sq (Adj) = 64.9% Which of the following is the best interpretation of the standard deviation of the residuals? The typical arm span is 161 centimeters. The typical foot length is 16.1 centimeters. The typical distance between the observed and predicted arm spans is 1.61 centimeters. The typical distance between the observed and predicted foot lengths is 1.61 centimeters. Op

n a regression analysis involving 30 observations, the following estimated regression equation was obtained. ŷ = 17.6 + 3.8x1 − 2.3x2 + 7.6x3 + 2.7x4 For this estimated regression equation, SST = 1,855 and SSR = 1,810. (a) At ? = 0.05, test the significance of the relationship among the variables.   Find the value of the test statistic. (Round your answer to two decimal places.)   Find the p-value. (Round your answer to three decimal places.) p-value =      Suppose variables  x1 and x4  are dropped from the model and the following estimated regression equation is obtained. ŷ = 11.1 − 3.6x2 + 8.1x3 For this model, SST = 1,855 and SSR = 1,755. (b) Compute  SSE(x1, x2, x3, x4). SSE(x1, x2, x3, x4)  =  (c) Compute  SSE(x2, x3). SSE(x2, x3) =    Find the value of the test statistic. (Round your answer to two decimal places.)   Find the p-value. (Round your answer to three decimal places.) p-value =

An automobile rental company wants to predict the yearly maintenance expense (Y) for an automobile using the number of miles driven during the year () and the age of the car (, in years) at the beginning of the year. The company has gathered the data on 10 automobiles and run a regression analysis with the results shown below:.   Summary measures       Multiple R 0.9689       R-Square 0.9387       Adj R-Square 0.9212       StErr of Estimate 72.218                 Regression coefficients         Coefficient Std Err t-value p-value Constant 33.796 48.181 0.7014 0.5057 Miles Driven 0.0549 0.0191 2.8666 0.0241 Age of car 21.467 20.573 1.0434 0.3314 Use the information above to estimate the annual maintenance expense for a 10 years old car with 60,000 miles.

In a regression analysis involving 30 observations, the following estimated regression equation was obtained. ŷ = 17.6 + 3.8xi – 2.3x2 + 7.6x3 + 2.7x4 For this estimated regression equation SST = 1805 and SSR = 1772. a. At a = 0.05, test the significance of the relashionship among the variables. SSE (to 1 decimal, if necessary) MSR (to 1 decimal, if necessary) MSE (to 2 decimals, if necessary) What is the value of the F test statistic (to 2 decimals)? Use Table 4 in Appendix B. What is the p-value? - Select your answer Using a = 0.05, what is your conclusion? - Select your answer - Suppose variables a1 and x4 are dropped from the model and the following estimated regression equation is obtained. ŷ = 11.1 – 3.6x2 + 8.1æ3 For this model SST = 1805 and SSR = 1,705. b. Compute SSE(x1, x2, X3, T4). (to 1 decimal, if necessary) c. Compute SSE(x2, x3). (to 1 decimal, if necessary)

Given the correlation coefficient 0.794 and the linear regression equation ŷ = 16.4 +1.58x, compute the coefficient of determination. p² Round to 4 decimal places. =