Question

In: Statistics and Probability

ABC Company has decided to use 20 test markets to examine the sensitivity of demand for...

ABC Company has decided to use 20 test markets to examine the sensitivity of demand for its new product, Hand Sanitizer, to various prices, as shown in the following table. Each market had approximately the same level of business activity and population.

Test Market Quantity sold (Thousands of Pens) Price Charged (cent)

1 20 50

2 21 50

3 19 55

4 18 60

5 20 60

6 14 65

7 16 65

8 20 70

9 12 70

10 14 80

11 12 70

12 10 70

13 14 65

14 16 90

15 18 45

16 16 70

17 20 65

18 12 80

19 18 70

20 10 50

Q.1. Using a linear regression model, estimate the demand function for ABC Company's new product, Hand sanitizer.

Q.2. Interpret the coefficient value of the independent variable of the estimated demand function.

Q.3. What will be the predicted/estimated sale for each price shown in column 2?

Q.4. Find the prediction interval at 95% for price of 70 cent.

Q.5. Interpret your prediction interval of Q.4.

Q.6. Conduct the hypothesis test at k=0.5:

(a) Set the null and alternative hypothesis

(b) Calculate standard deviation to calculate t-statistic

(c) Calculate t-statistic

(d) Find the critical value at k=.05 using the t-distribution table

(e) State the decision rule and apply your critical value to test the hypothesis

(f) Draw conclusion of your hypothesis test.

Q.7. Calculate the correlation coefficient for ABC Company.

Q.8. Find the value of coefficient of determination (r²).

Q.9. Interpret the coefficient of determination.

Solutions

Expert Solution

Coeff	SE	t-stat	lower t0.025(21)	upper t0.975(21)	Stand Coeff	p-value	VIF
b	14.961110	1.970633	7.592034	10.862955	19.059265	0.00000	1.88617e-7
X1	0.00914959	0.0320505	0.285474	-0.0575031	0.0758023	0.0285313	0.778078	1.000000

Predicted y

15.418590
15.418590
15.464338
15.510086
15.510086
15.555833
15.555833
15.601581
15.601581
15.693077
15.601581
15.601581
15.555833
15.784573
15.372842
15.601581
15.555833
15.693077
15.601581
15.418590
14.961110
14.961110
14.961110

ANOVA table

Source	DF	Sum of Square	Mean Square	F Statistic	P-value
Regression (between ŷiand yi)	1	1.127786	1.127786	0.0814955	0.778078
Residual (between yiand ŷi)	21	290.611344	13.838635
Total(between yiand yi)

orchestra answered 1 year ago

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