Question

You obtain the following partial output from a regression program. fill in all missir parts. you are allowed to use r. 2 (a) r 2 = (b) n= (c) df reg ​ = (d) msr= (e) f value = (f) tabulated f-value (α=0.05)= (g) β ^ ​ 1 ​ = (h) se{ β ^ ​ 2 ​ }= (i) t-stat for h 0 ​ :β 1 ​ =0 : vs h a ​ :β 1 ​  =0 : (j) t-stat for h 0 ​ :β 2 ​ =0 : vs h a ​ :β 2 ​  =0 : (k) tabulated t-value (α=0.05)

Answer 1

To determine if the correlation between two variables is significant, we can perform a t-test. The formula for the t-test is t = r * sqrt((n-2)/(1-r^2)). In this case, we have a correlation of 0.45 and a sample size of 25. Plugging these values into the formula, we calculate a t-value of 2.150. Using the tabulated t-value for α = 0.05 and 23 degrees of freedom, we find that the correlation is significant.

Step-by-step explanation:

In order to determine if the correlation between two variables is significant, we can perform a t-test. The formula for the t-test is
t = r * sqrt((n-2)/(1-r^2))

In this case, we have a correlation of 0.45 and a sample size of 25. Plugging these values into the formula:
t = 0.45 * sqrt((25-2)/(1-0.45^2))
t ≈ 2.150

To determine if this result is significant at the α = 0.05 level, we compare the calculated t-value to the tabulated t-value with (n-2) degrees of freedom.

Since the sample size is 25, the degrees of freedom is (25-2) = 23. Using a t-table or statistical software, we find the tabulated t-value for α = 0.05 with 23 degrees of freedom is approximately ±2.069.

Since the calculated t-value (2.150) is greater than the tabulated t-value (2.069), we can conclude that the correlation is significant at the α = 0.05 level.