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Chapter 9, Section 1, Exercise 005 Computer output for fitting a simple linear model is given...

Chapter 9, Section 1, Exercise 005

Computer output for fitting a simple linear model is given below. State the value of the sample slope for the given model.

In testing if the slope in the population is different from zero, identify the p-value and use it (and a 5 % significance level) to make a clear conclusion about the effectiveness of the model.

The regression equation is Y ⁢=87.0 -6.9 X

. Predictor Coef SE Coef T P

Constant 87.013 4.415 19.71 0.000

X -6.9023 0.8054 -8.57 0.000

what is the sample slope?

what is the p- value?

is the model effective?

Solutions

Expert Solution

Given ,

Regression equation : Y ⁢=87.0 - 6.9*X

Sample slope = -6.9023

We have to test if the slope in the population is different from zero.

So, hypothesis is ,

Where , is slope in the population.

From given table ,

P-value = 0.00

Significance level = = 5% = 0.05

Rejection rule : Reject null hypothesis if p-value less than .

It is observed that , p-value ( 0.00) is less than = 0.05

So reject null hypothesis.

i.e there is sufficient evidence to conclude that slope in the population is different from zero.

So, The model is effective

orchestra answered 1 year ago

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