Question

CHAPTER 4, QUESTION 14

Café Michigan's? manager, Gary? Stark, suspects that demand for mocha latte coffees depends on the price being charged. Based on historical? observations, Gary has gathered the following? data, which show the numbers of these coffees sold over six different price? values:

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Price	Number Sold
?$2.70	770
?$3.50	510
?$2.00	990
?$4.20	250
?$3.00	315
?$4.00	480

Using simple linear regression and given that the price per cup is ?$1.80?,

the forecasted demand for mocha latte coffees will be ____ cups ?(enter your response rounded to one decimal? place).

Answer 1

A simple linear regression is of the form

Y = b₀ + b₁ X

where b₀ is the intercept and b₁ is the slope

The regression equation is Y = 1450.87 - 277.85 X

when the price per cup is $ 1.80, the forecasted demand is

Y = 1450.87 - 277.85 * $ 1.80

Forecasted demand = 950.7 units

Output of regression analysis

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.822905
R Square	0.677173
Adjusted R Square	0.596467
Standard Error	178.2504
Observations	6
ANOVA
	df	SS	MS	F	Significance F
Regression	1	266594.7	266594.7	8.390549	0.044267
Residual	4	127092.8	31773.21
Total	5	393687.5
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	1450.874	318.5657	4.554393	0.010383	566.3933	2335.354	566.3933	2335.354
X Variable 1	-277.847	95.92047	-2.89664	0.044267	-544.165	-11.5296	-544.165	-11.5296