Statistics徵求統計高手

A student used multiple regression analysis to study how family spending (Y) is influenced by income (X1)

family size (X2)

and additions to savings (X3). The variables Y

X1

and X3 are measured in thousands of dollars. The following results were obtained.Degrees ofSum ofSourceFreedomSquaresFRegression345.963464.28Error112.6218PredictorCoefficientStandard ErrorConstant0.0136X10.79920.074X20.22800.190X3-0.57960.920Coefficient of determination = 0.946a.Write out the estimated regression equation for the relationship between the variables.b.What can you say about the strength of this relationship?c.Carry out a test of whether Y is significantly related to the independent variables. Use a .05 level of significance.d.Carry out a test to see if X3 and Y are significantly related. Use a .05 level of significance.
a.Write out the estimated regression equation for the relationship between the variables.Yhat＝0.0136＋0.7992*X1＋0.2280*X2－0.579*X3b.What can you say about the strength of this relationship?判定係數Coefficient of determination = 0.946

表示X1、X2、X3可以解釋Y的變異量達94.6%

表示具有很強的線性關係。

c.Carry out a test of whether Y is significantly related to the independent variables. Use a .05 level of significance.H0: 估計回歸方程式不顯著 v.s. H1:估計回歸方程式顯著檢定統計量F=[SSR/dfSSR]/[SSE/dfSSE]=[45.9634/3]/[2.6218/11]=64.2812拒絕域={F