Question

For a multiple regression analysis, we have two independent variables and one dependent variable with 15 observations each. The coefficient of determination value is 0.886. what is the test statistic to determine the validity of the corresponding regression model? a) 4.6316 b) 45.6316 c) 46.6316 d) 0.6316

Answer 1

Answer:

option A

Step-by-step explanation:

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Answer 2

Answer:

The correct answer is option C

Step-by-step explanation:

Given:

The coefficient of determination $R^{2}$ is 0.886.

There are 2 independent variables and one dependent variable with 15 (n) observations each.

Determine the test statistic for regression

The test statistic for regression is,

$\frac{M S R}{M S E}$

And,

$\begin{aligned}R^{2} &=\frac{S S R}{S S T} ----(i)\\1-R^{2} &=1-\frac{S S R}{S S T} \\1-R^{2} &=\frac{S S T-S S R}{S S T} \\1-R^{2} &=\frac{S S E}{S S T}-----(ii)\end{aligned}$

Compute the mean sum of squares

The mean sum of squares is,

$\begin{aligned} M S R &=\frac{S S R}{2} \\ M S E &=\frac{S S E}{n-3} \\ &=\frac{S S E}{12} \end{aligned}$

Now, divide the equation (i) by (ii),

$\begin{aligned} \frac{R^{2}}{1-R^{2}} &=\frac{S S R / S S T}{S S E / S S T} \\ \frac{R^{2}}{1-R^{2}} &=\frac{S S E}{S S R} \\ \frac{R^{2} / 2}{1-R^{2} / 12} &=\frac{S S E / 2}{S S R / 12} \\ \frac{12 R^{2}}{2\left(1-R^{2}\right)} &=\frac{M S R}{M S E} \\ \frac{12 R^{2}}{2\left(1-R^{2}\right)} &=F \\ F &=\frac{12(0.886)}{2(1-0.886)} \\ &=46.63157 \end{aligned}$

$\approx 46.6316$

The test statistics to determine the validity of the corresponding regression model is $46.6316$

The option C is correct answer.