Question

Considering \(Y\) as a dependent variable, a regression model is applied with three independent variables \(\mathrm{X} 1 \mathrm{X} 2\) and \(\mathrm{X} 3 .\) The results of the regression analysis are shown below:

Answer the following:

1. Define \(\mathrm{R}\) and \(\mathrm{R}\) Square.

2. What is the significance of \(\mathrm{F}\) test.

3. Which variable has the highest impact on Y.

4. Write the regression equation.

5. Calculate \(Y\) if \(X_{1}=10, X_{2}=20\) and \(X_{3}=5\)

Answer 1

1. \(\mathrm{R}=\) Correlation coefficient

\(\mathrm{R}\) is a statistical measure of the strength of the relationship between the relative movements of two variables.

Here, \(\mathrm{R}=0.969\)

Therefore, \(96.9 \%\) of strength in the relationship between two variables.

R square= coefficient of determination.

R square measures the proportion of variation in dependent variable is explained by independent variables.

Here, \(\mathrm{R}\) square \(=0.939\)

Hence, 0.939 proportion of variation in \(y\) is explained by \(x 3, x 4\) and \(x 5 .\)

2. The significance F gives the probability that the model is wrong.

Statistically, the significance \(\mathrm{F}\) is the probability that the null hypothesis is our regression model cannot be rejected.

3. X4 variable has the highest impact on y. Because t significance is less than alpha sonwe reject null hypothesis and support the claim. Also \(\beta\) corresponding \(\times 4\) is greater than other \(\beta\) 's.

4. The regression equation is,

$$ y=35.681-0.654 * x 3+0.233 * x 4+0.115 * x 5 $$

5. \(X 1=10, x 2=20, x 3=5\)

$$ y=35.681-0.654^{*} 5=32.41 $$