Given that the following demand relationship between the quantity demanded (Q) a

Question

Given that the following demand relationship between the quantity demanded (Q) and its per-unit price (P) is estimated by a simple regression equation on the basis of 20 observations, answer Questions 16 through 21: The corresponding ANOVA table shows only the sums of squares as follows: If the calculated t-value for the slope coefficient is -1.9, you would find the table value of t to be ____________ and thus, conclude to ____________ the null hypothesis of the slope coefficient being equal to zero at the 5%significance level. 1.7247; reject 1.7341; accept 1.7341; reject 2.1009; accept 2.1009; reject Based on the sums of squares given, the coefficient of determination is ____________ and the corresponding calculated F-statistic is _____________ 0.5714; 24 0.4286; 24 0.5714; 1.333 0.4286; 1.333 0.75; 1.333 Given that an F-test is to be done for the joint significance of coefficients, you would find that the degrees of freedom for the numerator and the denominator are respectively __________and ___________ 1; 19 1; 18 2; 20 2; 19 2; 18

Explanation / Answer

Question 19

We are given

Sample size = n = 20

So, degrees of freedom = n - 1 = 20 – 1 = 19

Significance level = alpha = 5% = 0.05

Critical t value = 2.1009 (By using t-table)

Absolute value of calculated t value is less than absolute critical t value, so we do not reject the null hypothesis.

So, correct answer is d.

Question 20

We are given

SSR = 200, corresponding df = 2 – 1 = 1

SSE = 150, corresponding df = 19 – 1 = 18

SST = SSR + SSE = 200 + 150 = 350, corresponding df = 20 – 1 = 19

Coefficient of determination = r^2 = SSR / SST = 200/350 = 0.571429

MSR = SSR/df = 200/1 = 200

MSE = SSE/df = 150/18 = 8.333333

F = MSR/MSE = 200/ 8.333333 = 24

F-statistic = 24

So, correct answer is a.

Question 21

We have

SSR = 200,

Numerator df = 2 – 1 = 1

SSE = 150,

Denominator df = 19 – 1 = 18

MSR = SSR/df = 200/1 = 200

MSE = SSE/df = 150/18 = 8.333333

So, correct answer is b.

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