Question

In: Statistics and Probability

The following ANOVA table was obtained when estimating a multiple regression model. ANOVA df SS MS...

The following ANOVA table was obtained when estimating a multiple regression model.

ANOVA	df	SS	MS	F	Significance F
Regression	2	188,246.80	94,123.40	35.2	9.04E-07
Residual	17	45,457.32	2,673.96

Total	19	233,704.10

a.	Calculate the standard error of the estimate. (Round your answer to 2 decimal places.)

s_e

b-1.

Calculate the coefficient of determination. (Round your answer to 4 decimal places.)

Coefficient of determination

b-2.

Interpret the coefficient of determination.

	The proportion of the variation in y that is explained by the regression model.
	The proportion of the variation in x that is explained by the regression model.

c.	Calculate adjusted R². (Round your answer to 4 decimal places.)

Adjusted R²

Expert Solution

Part a) :

The standard error of the estimate= S_e = SQRT( MS of Residual /Df of Resudual .)

MS of residual = 2673.96 and df of residual = 17 .

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Part b)-1 ) Calculate the coefficient of determination.

Coefficient of determination denoted by , R²

Formula for R² = SS Regression /SS total .

Coefficient of determination denoted by , R² = 0.8055

b-2. Interpret the coefficient of determination.

The proportion of the variation in y that is explained by the regression model.

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Part c ) Calculate adjusted R².

p= number of parameter , N= total sample size

df for Regerssion =p - 1 and here df for regression is as 2

So , p - 1 = 2 ==>>>p = 3

And df for total =N-1 and here df for total =19 .

So , N-1 = 19 ==>>N= 20 .

orchestra answered 2 years ago

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