In a regression analysis involving 30 observations, the following estimated regression equation was obtained. 5 = 17.6 + 3.8x1 - 2.3x2 + 7.6x3 + 2.7x4 For this estimated regression equation SST = 1805 and SSR = 1,748. a. At = 0.05, test the significance of the relationship among the variables. SSE 57 (to 1 decimal, if necessary) MSR 437 (to 1 decimal, if necessary) MSE 22.8 (to 2 decimals, if necessary) What is the value of the F test statistic (to 1 decimal)? 19.2 What is the p-value? greater than .10 Using = .05, what is your conclusion? Conclude the relationship is significant b. Suppose variables x1 and x4 are dropped from the model and the following estimated regression equation is obtained. 5 = 11.1 - 3.6x2 + 8.1x3 For this model SST = 1805 and SSR = 1,705. Compute SSE(x1, x2, x3, x4) 100 (to 1 decimal, if necessary) Compute SSE(x2, x3) (to 1 decimal, if necessary) c. Use an F test and = .05 to determine whether x1 and x4 contribute significantly to the model. What is the value of the F test statistic (to 2 decimals)? What is the p-value? What is your conclusion about the two variables x1 and x4?
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To test the significance of the relationship among the variables, we need to perform an F test. The null hypothesis is that there is no significant relationship among the variables, and the alternative hypothesis is that there is a significant relationship. The Show more…
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In 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 = 1,805 and SSR = 1,770. (a) At α = 0.05, test the significance of the relationship among the variables. State the null and alternative hypotheses. H0: β1 = β2 = β3 = β4 = 0 Ha: 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.) State your conclusion. Reject H0. We conclude that the overall relationship is significant. 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 = 1,805 and SSR = 1,695. (b) Compute SSE(x1, x2, x3, x4). (c) Compute SSE(x2, x3). (d) Use an F test and a 0.05 level of significance to determine whether x1 and x4 contribute significantly to the model. State the null and alternative hypotheses. H0: β1 = β4 = 0 Ha: 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.) State your conclusion. Reject H0. We conclude that x1 and x4 contribute significantly to the model.
Dominador T.
The following estimated regression equation is based on 10 observations: 29.1270 + 0.5906x1 + 0.498032. Here, SST = 6,500.625, SSR = 6,025.625, R^2 = 0.0734, and R^2 adjusted = 0.0696. a. Compute MSR and MSE (to 3 decimals): MSR = SSR / k = 6,025.625 / 2 = 3,012.812 MSE = SSE / (n - k - 1) = (SST - SSR) / (n - k - 1) = (6,500.625 - 6,025.625) / (10 - 2 - 1) = 475 / 7 = 67.857 b. Compute F and perform the appropriate F test (to 2 decimals). Use α = 0.05. Use the F table. F = MSR / MSE = 3,012.812 / 67.857 = 44.38 The p-value is . At α = 0.05, the overall model is . Perform a t test for the significance of B1 (to 2 decimals): Use α = 0.05. Use the t table: t8. The p-value is . At α = 0.05, there is relationship between y and x1. d. Perform a t test for the significance of B2 (to 2 decimals): Use α = 0.05. Use the t table: t82. The p-value is . At α = 0.05, there is relationship between y and x2.
Madhur L.
Given are five observations for two variables, x and y. xi 1 2 3 4 5 yi 4 7 6 11 14 The estimated regression equation is y = 1.2 + 2.4x. Compute the mean square error using the following equation (to 3 decimals). Compute the standard error of the estimate using the following equation (to 3 decimals). Compute the estimated standard deviation b1 using the following equation (to 3 decimals). Use the t-test to test the following hypotheses (α = .05): Compute the value of the t-test statistic (to 2 decimals). The p-value is: - Less than .01 - Between .01 and .02 - Between .02 and .05 - Between .05 and .10 - Between .10 and .20 - Between .20 and .40 - Greater than .40 Item 5: Use Table 1 of Appendix B. What is your conclusion? - Conclude a significant relationship exists between x and y - Cannot conclude a significant relationship exists between x and y Item 6: Use the F-test to test the hypotheses in part (d) at a .05 level of significance. Complete the F table below. Calculate the Sum of Squares (to 1 decimal), the Mean Squares (to 3 decimals), and the F ratio (to 2 decimals). Source of Variation Degrees of Freedom Sum of Squares Mean Square F Regression Error Total
Sri K.
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