Question

Use the following to answer the next 3 questions. Recent research efforts in your company have focused on the problem of predicting / explaining a manufacturer’s market share (as a percentage) by using information on the quality of its product (on a scale of 0 to 100). The following is the simple linear regression output for such a study. Please refer to them in order to answer the following questions.

Regression summary output for market share vs. product quality:

SUMMARY OUTPUT
Regression Statistics
R Square	?
Adjusted R Square	?
Standard Error	?
Observations	13
ANOVA
	df	SS	MS	F
Regression	1	128.3320929	128.3320929	129.52518
Residual	11	10.8986763	0.990788754
Total	12	?
	Coefficients	Standard Error	t Stat	P-value
Intercept	-3.056581	0.97101977	-3.14780504	0.0092784
X Variable 1	0.186634	0.01639882	?	?

Interpret the meaning of β0 in the context of the problem.

a)Expected value of the market share when the product quality is zero

b)Expected value of the product quality when the market share damage is zero

c)Expected increase in the market share when the product quality goes up by one unit

d)Expected increase in the product quality when the product quality goes down by one unit

Interpret the meanings of β1 in the context of the problem.

a)Expected value of the market share when the product quality is zero

b)Expected value of the product quality when the market share damage is zero

c)Expected increase in the market share when the product quality goes up by one unit

d)Expected increase in the market share when the product quality goes down by one unit

Obtain the coefficient of determination (R-squared)

a)0.99

b)0.18

c)0.92

d)0.88

Answer 1

Solution:

a) Interpretation of intercept  

When product quality (X)equal to zero then is the mean or expected value of the market share. When product quality (X) not equal to zero then has not physical interpretation.

Expected value of the market share when the product quality is zero.

Option A is correct .

b ) Interpretation of slope  

When one unit change in product quality (X) then the average or expected change in market share.

Also When one unit increases in product quality then the expected increases by market share by 0.186634.

Expected increase in the market share when the product quality goes up by one unit.

Option C is correct .

c) Given :

Sum of square of regression = SSR = 128.3320929

Sum of square of error=SSE = 10.8986763

Sum of square of total = SST = SSR + SSE

SST = 128.3320929 + 10.8986763

SST = 139.23076

The coefficient of determination can be determined by using the formula

Option C is correct.