Question

The following table shows worldwide sales of smartphones and their average selling prices in 2012, 2013, and 2017:

Year	2012	2013	2017
Selling Price p ($100)	4	3	2
Sales q (billions of units)	0.5	1	2.10

a.  Find the regression line for sales, q, in terms of selling price, p. (round coefficients to one decimal place). (3)

b.  What is the slope of the line and interpret it in context of the problem. (2)

c.  Use the regression line to estimate the demand ( in billions of units sold) when the selling price was $350. (3)

Answer 1

(a)

Excel regression summary output:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.98
R Square	0.96
Adjusted R Square	0.91
Standard Error	0.24
Observations	3
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1.28	1.28	21.33333	0.135737209
Residual	1	0.06	0.06
Total	2	1.34
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	3.6	0.538516481	6.685032	0.09453	-3.242500657	10.44250066
p	-0.8	0.173205081	-4.6188	0.135737	-3.000779217	1.400779217

Regression equation: q = 3.6 - 0.8 x p

(b)

Slope = - 0.8

It means that when price increases (decreases) by $1,000, Sales decreases (increases) by 0.8 billion units.

(c)

When p = 3.5,

q = 3.6 - 0.8 x 3.5 = 3.6 - 2.8 = 0.8 billion