In a certain industry, costs are believed to be approximately linearly related t
ID: 3292395 • Letter: I
Question
In a certain industry, costs are believed to be approximately linearly related to output. The following data show the cost of production (in thousands of dollars) and the number of units produced for eight firms in the industry (n = 8): Using a T - Test, test whether the slope term is significantly different from zero. That is, test H_0: beta_1 = 0, vs H_A: beta_1 notequalto 0 at alpha = 05. (2-tailed test). b. The ANOVA table below comes from the equation above, and is incomplete. Fill in the table, & test the hypothesis H_0: beta_1 = 0, vs. H_A: beta_1 notequalto 0, at alpha = 05, using the F test to test whether all the independent variables (1 variable in this case) affect Y. You are given: sigma Y_i^2 = 255883 sigma X_i Y_i = 99830 sigma X_i = 540 sigma Y_i = 1415 sigma X_i^2 = 39850 ALSO: nX^2 = 36450 nY^2 = 250278.1Explanation / Answer
2)a)
TS = 1.26985/0.07742 = 16.40144
df = n-2 = 6
p-value = 2 P(t > 16.40144) = 0.00000327 << 0.05
hence we reject the null and comclude that b1 is significant
2b) df_reg = 1 , df_error = n-2 =6
MS = SS/df
F = MS_reg/MS_Residual
SS_total = SS_reg + SS_residual
SS_Total = sum Y_i^2 - n (Y_bar)^2 = 5604.875
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