In a multiple regression model, when adding more predictors will R-squared-SSR/S

Question

In a multiple regression model, when adding more predictors will R-squared-SSR/SST will Not decrease Not increase May decrease or increase or stay the same When testing H0: beta_1 = beta_2 = 0 The corresponding F-test will have degrees of freedom and n-p-1 When someone wished to create an interval around a singular future value, they should Create a confidence interval Prediction interval A multiple regression model with two predictors, when testing HO: beta_1 = 0 You are testing That x_1 is a significant predictor That x_1 is significant above and beyond x2

Explanation / Answer

Q1. R2 is coefficient of determination : This indicate percent of variation is Y are explained by x variable(s).

R2 = 0 means dependent variable (y) can not be predicted by independent variable ( x )

R2 = 1 Means dependent variable (y) is predicted by independent variable (x) without any error.

Hence greater the value of R2 , less chances of having error.

Adding more predictors will decrease the error and increases the R2 .

Hence the correct option is Not decrease.

Q2.

In regression ANOVA will have F as F(df of regression, df of error )

So here we have 3 varaibles y , x1,x2 . Hence degrees of freedon for regression = 3-1 = 2

Hence the correct option is 2.

Q3. Confidence interval will give us interval for the value which have computed. Where prediction interval will give us the interval for the value which we will have in future.

Hence the correct option is Prediction interval

Q4. In multiple regression testing sinngle slope means we are finding that the perticular indepenent variable is significantly related to y variable or not.

Hence the correct option is : That x1 is a significant predictor.

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