Question

Suppose that we regress the Number of students admitted to CIU on advertisement expenses by CIU and we found the following results

ANOVA

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

502.916684

4.13242072

121.700262

2.0846E-94

494.695983

511.137385

X Variable 1

0.21831397

0.0771261

2.83061067

0.00584148

0.06488558

0.37174235

A. What is the value of the coefficient of B? Interpret the meaning of the result

B. What is the 95% confidence interval for b ?

C. From the result above, at P-value = 5% can we reject the hypothesis that CIU”s advert expenses have no effect on the number of students admitted into CIU? If yes, why and if no, why not?

Answer 1

From the result above we can answer following questions

Part a) -

The equation of the estimated regression line is

Number of students = 502.916684 + 0.21831397* CIU's advertisement expenses

The value of the coefficient of B is 0.21831397.

We can interpret the coefficient as if the CIU's advertisement expenses are increased by 1 unit then the number of students is expected to increase by 0.21831397 units.

Part b) - 95% confidence interval for b is { 0.06488558, 0.37174235 }

Part c) -

Null hypothesis: H₀: CIU's advertisement expenses have no effect on the number of students admitted.

Alternative hypothesis: H₁: CIU's advertisement expenses have a significant effect on the number of students admitted.

Decision rule is we reject H₀ at 5% level of significance if p-value > 0.05.

P-value for this test is 0.00584148.

As this p-value < 0.05 we do not have enough evidence to reject H_0.

Hence, we do not reject the hypothesis that CIU's adevertisement expenses have no effect on the number of students admitted into CIU.

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