Question

In a regression analysis of a first-order model involving 3 predictor variables and 25 observations, the following estimated regression equation was developed.

= 12 - 18x1 + 4x2 + 15x3

Also, the following standard errors and the sum of squares were obtained.

sb1 = 3	sb2 = 6	sb3 = 7
SST = 4900	SSE = 1296

If we are interested in testing for the significance of the relationship among the variables (i.e., significance of the model), the critical value of F at α = .05 is

1. 2.76

2. 3.10

3. 3.07

4. 4.87

Answer 1

In a regression analysis of a first-order model involving 3 predictor variables and 25 observations, the following estimated regression equation was developed.

Respose = 12 - 18x1 + 4x2 + 15x3

Also, the following standard errors and the sum of squares were obtained.

sb1 = 3, sb2 = 6, sb3 = 7, SST = 4900 and SSE = 1296

Now we are interested in testing for the significance of the relationship among the variables (i.e. significance of the model).

[ Formula:-

For a regression model with k predictor variable and n observations,

i) Numerator DF of F-statistic = k

ii) Denominator DF of F-statistic = (n - k -1) ]

So for this problem form given data we get, predictor variable k = 3 and number of total observations n =25

Numerator DF of F-statistic = k = 3 [applying formula (i)]

Denominator DF of F-statistic = (n - k -1) = (25-3-1) = 21 [applying formula (ii)]

Now we want to find the critical Value of F-statistic with DF = (3, 21) at

[ Value are getting from F-table with corresponding and DF = (3, 21) ]

Answer:- Correct answer is " 3rd Option. (3.07) "