Question

15. A company’s top brand shows the following data of its unit selling price and its corresponding sales amount:

Unit Price($)	Sales Amount($Million
11	1.5
13	1.2
14	0.8
12	1.3
15	0.7

1) Find a simple linear regression model with X = unit selling price and Y = sales amount.

2) If the company lowers its selling price to $10, what would be the expected sales amount?

3) Based on the regression model you find, estimate the change of sales amount (increase or decrease) according to one dollar increase of product price.

4) As you know, the sales amount is affected by many different variables such as price, advertising, quality, product design, etc. what would you think how much the product price variable has an impact on sales in terms of percentage?

Answer 1

1)

Unit Price	Sales Amount
11	1.5
13	1.2
14	0.8
12	1.3
15	0.7

The independent variable is Unit Price

and the dependent variable is Sales Amount

In order to compute the regression coefficients, the following table needs to be used:

	Unit Price	Sales Amount	Unit Price*Sales Amount	Unit Price2	Sales Amount2
	11	1.5	16.5	121	2.25
	13	1.2	15.6	169	1.44
	14	0.8	11.2	196	0.64
	12	1.3	15.6	144	1.69
	15	0.7	10.5	225	0.49
Sum =	65	5.5	69.4	855	6.51

Based on the above table, the following is calculated:

Therefore, based on the above calculations, the regression coefficients (the slope m, and the y-intercept n) are obtained as follows:

Therefore, we find that the regression equation is:

2)

3)

one dollar increase of product price will decrease the sales amount by $0.21 million.

4)

Now, the correlation coefficient is computed using the following expression:

Then, the coefficient of determination, or R-Squared coefficient (R^2),

is computed by simply squaring the correlation coefficient that was found above. So we get:

Therefore, based on the sample data provided, it is found that the coefficient of determination is R^2=0.9587.

This implies that approximately 95.87% of variation in the sales amount is explained by the unit selling price.

please like)