Question

1. A sample of 12 observations collected in a regression study on two variables, x(independent variable) and y(dependent variable). The sample resulted in the following data.

   SSR=77, SST=88,  summation (x_i-xbar)²=23, summation (x_i-xbar)(y_i-ybar)=44.

   Calculate the t test statistics to determine whether a statistically linear relationship exists between x and y.

2. A sample of 7 observations collected in a regression study on two variables, x(independent variable) and y(dependent variable). The sample resulted in the following data.

   SSR=24, SST=42

   Using a 0.05 level of significance, we conclude that there is a significant linear relationship between x and y. (Enter 1 if the conclusion is correct. Enter 0 if the conclusion is wrong.)

3. A sample of 6 observations collected in a linear regression study on three variables, x_1(independent variable), x_2(independent variable) and y(dependent variable). The sample resulted in the following data.

   SSR=72, SST=88

   Calculate the F test statistics to determine whether a statistically linear relationship exists between x and y.

4. A sample of 12 observations collected in a regression study on three variables, x_1(independent variable), x_2(independent variable) and y(dependent variable). The sample resulted in the following data.

   SSR=60, SST=86

   Calculate an unbiased estimate of the variance of the error term epsilon.

5. A sample of 10 observations collected in a regression study on three variables, x_1(independent variable), x_2(independent variable and y(dependent variable). The sample resulted in the following data.

   SSR=26, SST=47

   Using a 0.01 level of significance, we conclude that the regression model is significant overall. (Enter 1 if the conclusion is correct. Enter 0 if the conclusion is wrong.)

Expert

Answer 1

Q 1)

We are given :

SSR = 77

SST = 88

Sample size n = 12

Null Hypothesis , there is no linear relationship between X and Y

Alternative Hypothesis

Under H0, the test statistic is

Where

b₁ - slope of regression line

-Estimate of the standard error of the least square slope

- Sample Standard error of the estimate

SSE = SST-SSR = 88-77 = 11

The test statistic is