Question

4. Testing for significance Aa Aa 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: 0.04 + 0.28X1 + 0.84X2-0.06x3 + 0.14x4 y She would like to conduct significance tests for a multiple regression relationship. She uses the F test to determine whether a significant relationship exists between the dependent variable and She 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 Degrees of Freedom Mean Source of Variation Regression (SSR) Error (SSE) Total (SST) Sum of Squares 41.7125 95.6105 137.3230 Square F value p-value 0.0004 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 a.05 is Use the Distributions tool to help you answer some of the questions that follow Select a Distribution Distributions 01 23 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 B2 0 Parameter Estimates Parameter Standard Variable Estimate Error t value p-value 0.04 0.28 0.84 -0.06 0.14 Constant 0.18 0.27 0.35 0.17 0.17 0.22 8267 1.04 3029 7277 -0.35 4158 0.82 X4 The t tests conducted at significance level α = .05 for each variable coefficient show that the following independent variables are significant: None of them X2 only x1 and xz X1,X2, and x3 The following table gives sample correlations between all possible pairings of variables in this model. Sample Correlations y X1X2X3 X4 y 1.00 0.48 0.52 -0.09 0.08 X1 0.48 1.00 0.73 0.15 0.02 x2 0.52 0.73 1.00 -0.04 -0.07 X3 0.09-0.15 1.000.11 0.04 x4 0.08 0.02 --0.11 1.00 0.07 The sample correlation of -0.15 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

The fill in the blanks are

(a) The set of all independent variables

(b) Each individual independent variables

(c) Overall

(d) T test is for inividual

f)

	SS	df	MS	F-value	p-value
regression	41.7125	4	10.42813	5.998785437	0.000444
error	95.6105	55	1.738373
total	137.323	59

MSR = 10.4281

MSE = 1.7384
F = 5.9988

g)

The F - test is significant at alpha = 0.05

h)

	estimate	standard error	t-value	p-value
x2	0.84	0.35	2.4	0.019807746

(i) Only x2

(j) Only x2.

(i) Highly Correlated

(i) A phenomenon callled "Multicollinearlity".

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