Question

Question 3

Due to the competition from Pepsi, Coca-Cola attempted to change its old recipe. Surveys of Pepsi drinkers indicated that they preferred Pepsi because it was sweeter than Coke. As a part of the analysis that led to Coke’s ill-fated move, the management of Coca-Cola performed extensive surveys in which consumers tasted various versions of the new Coke. Suppose that a random sample of 200 cola drinkers was given various versions of the Coke with different amount of sugar. After tasting the product, each drinker was asked to rate the taste quality. The possible responses were as follows:

1=poor; 2 = fair; 3 = average; 4 = good; 5 = excellent.

The responses (ratings) and sugar content (percentage by volume) of the version tested are given below

Rating	Sugar
1	6
1	9
4	21
4	20
1	6
5	15
1	5
5	20
5	23
3	13
3	7
1	5
1	6
4	15
3	14
3	12
1	5
1	4
5	17
4	12
3	16
1	8
4	18
3	12

(e) Construct and interpret the 95% confidence interval for β1

(f) Predict the expected rating of Coca-Cola for the sugar level of 9 (percentage per volume).

(g) How much is the coefficient of determination and interpret it?

(h) How much is adjusted R-square? When do you use adjusted R-square?

( I ) How much is the standard error of the estimate? Is it a good model based on this criterion?

Answer 1

By using MS EXCEL DATA ANALYSIS TOOL PACK WE HAVE

SOLUTION E] 95% CONFIENCE INTERVAL is ( 0.1822, 0.2889)

Interpretation: You can be 95% confident that the true population coefficent () falls between 0.1822 and 0.2889.

SOLUTION F] FOR X=9

SOLUTION G] COEFFICIENT OF DETERMINATION IS R SQUARED= 0.7923

INTERPREATION: 0.7923 indicates that the model explains 79.23% of the variability of the response data( rating) around its mean.

SOLUTION H] ADJUSTED R SQUARE= 0.7829

The adjusted R-squared is adjusted for the number of explanatoryin the model. We use it when we add any new eplanatory variable .

SOLUTION I] Standard error of estimte se= 0.7268

It tells the average distance that the observed values of y fall from the regression line. So when it is SMALL model is better.

Here se= 0.7268 so model is better .