Instructions Full work must be shown for each example or no

Instructions: Full work must be shown for each example or no credit will be awarded. Explain each result that you provide. Keep your solutions neat and do your best to conform to the format of the exam. The answer to each question should be typed right after the specific question and for full credit it should be complete and correct.

Q6. (30 POINTS)One of the stores is a proud sponsor of the college soccer team. They constantly try to raise money for the team and they want to determine if there is any type of relationship between the amount of contribution and the years that the alumnus has been out of school.

Years (X)  1  5  310 6 6 2

Contribution (Y)25010011007080175

Using Excel construct a scatter plot. Discuss the output of the scatter plot.   

Give (or calculate) the correlation coefficient.   

Give (or calculate) the coefficient of determination.

Give (or calculate) the regression equation coefficients; Give the equation of regression.

e. (very important)

Based on the above values, in detail draw the conclusion:

Discuss the correlation coefficient r

Discuss the coefficient of determination r2  

Discuss in detail the meaning of the regression equation (x=0; y=0)

f. How much would be the contribution of a student who graduated 7 years ago? After how many years after graduations the alumni will stop contributing.

Solution

From Excel

e)

Correlation coefficient r=0.9823

there is 98% correlation between two variables.

coefficient of determination.=0.9650

96% variation between to variables.

The regression equation is y=122.92+3.143(x)

where y is contribution and x is years

f) contribution of a student who graduated 7 years ago

y=122.92+3.143(7)=144.921