Using the multiple regression output below, determine the following: Multiple R
ID: 3074428 • Letter: U
Question
Using the multiple regression output below, determine the following: Multiple R 0.459837234 0.211450282 0193364279 R Square d R Square Standard Erro 5 28.643644895.728729 11.69138 218 106 8191439 0.489996 223 135 46278199 5.06E-10 Regression Residual otal Coefficents Standard Emor t Stat P-alue Lower 9596 upper 90% ntercept HSM HSS HSE SATM 0.326718739 0.399996431 0.816804 0414932 0 461636967 1.11507 444 0.14596108 0.039260974 3.717714 0.000256 0068581358 0.223340801 0.03590532 0037798412 0949916 0.343207 -003859183 011040247 0.055292581 0039568691 1397382 0.163719 0 022693622 0.133278785 0.000843593 0.000685657 1.376187 0.170176 0000407774 0.002294959 441 Part (a): Assuming HSM, HSS, HSE, SATM, and SATV are x1, X2, X, X4, and x respectively, what is the equation of the fitted regression line? Part (b): Is there a linear relationship between the independent and dependent variables? Confirm this from hypothesis testing. Part (c): Find2.Explanation / Answer
Solution(a)
In coefficient tables, we can find regression euqation which is as follows:
Y = b0 + b1*X1 + b2*X2 + b3*X3 + b4*X4 + b5*X5
Where b0 is intercept of regression line
b1, b2, b3, b4 and b5 are coefficients
So regression line can be written as
Y = 0.3267 + 0.14596 HSM + 0.03590 HSS + 0.05529 HSE + 0.00064 SATM + 0.00040 SATV
Here X1 is HSM, X2 is HSS, X3 is HSE, X4 is SATM and X5 is SATV.
This is regression equation.
Solution(b)
As we can see from the anova table that Significance or p-value is 0.000000005 which is less than 0.05 or 95% confidence level, so p-value is less than alpha value so we will reject our null hypotheis, which means that there is a linear relationship between the independent and dependent variables.
Solution(c)
r2 is coefficient of determination which tells that how much variance in dependent variable is explained by this regression model.
Here R2 = 0.2114
So this model only explain 21.14% variability explained by this model in dependent variable.
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