Question

Consider a multiple regression model of the dependent variable y on independent variables x1, X2, X3, and x4: Using data with n 60 observations for each of the variables, a student obtains the following estimated regression equation for the model given: y0.35 0.58x1 + 0.45x2-0.25x3 - 0.10x4 He would like to conduct significance tests for a multiple regression relationship. He uses the F test to determine whether a significant relationship exists between the dependent variable and He uses the t test to determine whether a significant relationship exists between the dependent variable and The F test is a test for significance, while the t test is a test for significance The sum of squares due to regression (SSR), the sum of squares due to error (SSE), and the total sum of squares (SST) for the multiple regression are shown in the following table. Analysis of Variance Mean Degrees of Source of Variation Regression (SSR) Error (SSE) Total (SST) Sum of Squares 38.5116 128.4310 166.9426 Freedom Square F value p-value 0.0054 Go through the following steps to complete the table: 1. Select the appropriate degrees of freedom for the three sums of squares. 2. Select the appropriate values for the mean square due to regression (MSR), the mean square due to error (MSE), and the F test statistic. The F test conducted at significance level α-.05 is Use the Distributions tool to help you answer some of the questions that follow Select a Distribution Distributions 0 The following table shows the estimates of the model parameters with the relevant statistics. Complete the table by selecting the appropriate value and p-value for the t statistic for the test of B20 Parameter Estimates Parameter Standard Variable Estimate Error 0.20 0.38 0.50 0.20 0.17 t value p-value .0857 Constant 0.35 0.58 0.45 0.25 0.10 1.75 1.53 1317 X2 2166 1.25 X3 0.59 .5576 4 The t tests conducted at significance level α = .05 for each variable coefficient show that the following independent variables are significant: None of them O X1 and X2 2 only OX1, X2, and x3 The following table gives sample correlations between all possible pairings of variables in this model Sample Correlations X2 X3 X4 У 1.00 0.42 0.43-0.19-0.02 X1 0.42 1.00 0.74 -0.06 0.13 X2 0.43 0.74 1.00 -0.15 -0.03 X3 0.19 -0.06 1.00-0.14 0.15 0.14 1.00 X4-0.02 0.13 0.03 The sample correlation of -0.06 between x1 and x3, for example, is shown in the cell located at the x1 row and X3 column (or, equivalently, at the x3 row and x1 column) The table given shows that the independent variables X1 and x2 have substantial correlation with y. However, the t tests for individual significance show that correlated with each other, a phenomenon called significant. This is because X1 and X2 are

Answer 1

mdependent ahe 2. 8322 5.59 o o 32 S116 3 eswo Todal CSST) ICC.42 59 29.u31o 56 2.2934 men henemena ns called mola celaen