Regression analysis was applied between sales data (in $1,000s) and advertising data (in $100s) and the following information was obtained.

~
y = 12 + 1.8x

n = 17
SSR = 225
SSE = 75
sb1 = 0.2683


Refer to Exhibit 12-3. The critical F value at a = 0.05 is

a. 3.59

b. 3.68

c. 4.45

d. 4.54

To determine the critical F value at a significance level of 0.05, we need to consult the F-distribution table or use statistical software.

The F-statistic is calculated as the ratio of the Mean Squares for regression (SSR) to the Mean Squares for error (SSE). In this case, SSR is given as 225 and SSE is given as 75.

To calculate the F-statistic, we use the formula:

F = (SSR / k) / (SSE / (n - k - 1))

Where k is the number of independent variables (in this case, 1), and n is the number of observations (in this case, 17).

Plugging in the values:

F = (225 / 1) / (75 / (17 - 1 - 1))
F = 225 / 75
F = 3

Next, we need to find the critical F value at a = 0.05. This value depends on the degrees of freedom for the numerator (k) and denominator (n - k - 1). In this case, k = 1 and (n - k - 1) = (17 - 1 - 1) = 15.

Using a statistical table or software, we find that the critical F value at a = 0.05, with degrees of freedom (1, 15), is approximately 4.54.

Therefore, the correct answer is option d. 4.54.