Question

The director of an alumni association wants to determine whether there is any type of relationship between the amount of an alumni's contribution (in dollars) and the number of years the alumnus has been out of school. Based on the data below, decide if the correlation between the number of years and the amount of the contribution is significant at the alpha value of 0.05.

Years x	1	3	5	10	6	9
Contribution y	640	290	170	45	70	80

a)       Determine the line of best fine y = a + bx

b)      When x = 8 what is y and what does it mean in this context.

Answer 1

The correlation coefficient is given by

From the given data, we have the following information

  

For alpha = 0.05 and the number of pairs = 6, the critical value of the correlation coefficient is 0.812.

Since the correlation coefficient is greater than 0.812, hence it is significant.

a) In order to know the line of best fit, we need to know the normal equations.

Let the line of best fit be

y = a + bx

Then, the normal equations are

--------------------------(I)

and

-------------------------(II)

Putting the values, we have

equation (i)

equation (ii)

Solving the two simultaneous equations, we have

a = 539.44

b = -57.107

Hence, the line of best fit is

b) Putting x = 8 in the given line, we get

Meaning - From the line of best fit, we can predict that if the alumni is 8 years old, then he is predicted to contribute

82.584 dollars.

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