Question

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 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.

Answer 1

Dear student, we can answer only four subparts at a time, please help to upload other parts separately.

1.

We will be applying the Linear regression model here, it can be done by using the function LINEST(y_value, x_value, TRUE, TRUE) where y_values contain values of Price Charged here and x_values have Quantity sold values.

Select 5 rows and 2 columns and then write the formula in the first cell and after that, press Shift + Ctrl + Enter.   

The equation comes out to be -

Price = 83.18 - 1.14*Quantity    

2.

When there is an increase of 1 unit in the quantity sold, there is a decrease of 1.14 units in the Price charged.

3.

It's shown in the excel file.

Test Market	Quantity sold (Thousands of Pens)	Price Charged (cent)	Price(predicted)
1	20	50	60.45455
2	21	50	59.31818
3	19	55	61.59091
4	18	60	62.72727
5	20	60	60.45455
6	14	65	67.27273
7	16	65	65
8	20	70	60.45455
9	12	70	69.54545
10	14	80	67.27273
11	12	70	69.54545
12	10	70	71.81818
13	14	65	67.27273
14	16	90	65
15	18	45	62.72727
16	16	70	65
17	20	65	60.45455
18	12	80	69.54545
19	18	70	62.72727
20	10	50	71.81818

d)

The correlation coefficient comes out to be -0.35714.