A multiple regression analysis produced the following tables

A multiple regression analysis produced the following tables.

Predictor

Coefficients

Standard Error

t Statistic

p-value

Intercept

752.0833

336.3158

2.236241

0.042132

x1

11.87375

5.32047

2.231711

0.042493

x2

1.908183

0.662742

2.879226

0.01213

ANOVA

Source

Df

SS

MS

F

p-value

Regression

2

203693.3

101846.7

6.745406

0.010884

Residual

12

181184.1

15098.67

Total

14

384877.4

What is your overall hypothesis? Do you reject it at a = 5%? What about if a = 1%

What is the coefficient of determination?

What are your hypotheses about individual parameters? Do you reject them?

What is the standard error estimate?

Predictor	Coefficients	Standard Error	t Statistic	p-value
Intercept	752.0833	336.3158	2.236241	0.042132
x1	11.87375	5.32047	2.231711	0.042493
x2	1.908183	0.662742	2.879226	0.01213

Solution

1) Overall hypothesis

P value = 0.010

for a =5% because of P value of < 0.05

so we can reject Null hypothesis (Accpet Model)

but for a = 1% because of P value is > 0.01

We have to accept null hyphpothesis (Reject Model)

2)

Coeff. of Determination = 1 - SS_R/SS_Total

R^2 = (1 - 203693.3/384877.4)*100%

R^2 = 47.07%

3)

P value of rejecting X1 < 0.05

and also P value of rejecting X2 < 0.05

So we can reject both null hypothesis

So both parameters are significance

4) standard error of the estimate is the square root of the Residual Mean Square.

standard error of the estimate = sqrt(15098.67) = 122.87

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