6．What is the lower limit of a 95 percent confidence interval for the predicted value of company sales (Y) given industry sales of $3,300?

A)   1,337.06.

B)   778.47.

C)   827.80.

D)   160.00.

The correct answer was B)

The predicted value is Ŷ = -94.88 + 0.2796 * 3,300 = 827.8.

The lower limit for a 95% confidence interval = Ŷ - t_cs_f = 827.8 - 3.182 * 15.5028 = 827.8 – 49.33 = 778.47 (Interim calculations below).

The critical value of t_c at 95% confidence and 3 degrees of freedom is 3.182.

The standard error of the forecast, s_f²= s_e²[1 + 1/n + (X - X)²/(n - 1)s_x²], where

s_e² = MSE = 200.17
n = 5
X = 3,300
X = 16,450/5 = 3,290
s_x² = Σ(X_i - X)² / (n - 1) = 152,000 / 4 = 38,000

Substituting, s_f²= 200.17 * {1 + 1/5 + (3,300 – 3,290)² / [(5 - 1) * 38,000]} = 240.335691

s_f = 15.5028