The director of an alumni association for a university wants to look at the relationship between the number of years since graduation and the amount of monetary contribution an alumnus makes to the university. He collects data on 50 alumni who have made contributions this year. The number of years since graduation has a mean of 5.5, and the amount of contribution has a mean of $132. Based on the least squares regression line fitted to the data, it is found that for every year increase since graduation, the contribution is expected to drop by $45.

Predict the amount of contribution made by an alumnus who graduated 5 years ago.

x-bar=5.5

y-bar=132
b1=-45

b0=132-(-45x5.5)= 379.5

x=5

y-hat=379.5-45x5 = 154.5

contribution amount= $154.5

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To predict the amount of contribution made by an alumnus who graduated 5 years ago using the least squares regression line, we can use the following steps:

Step 1: Define the variables:
Let X be the number of years since graduation.
Let Y be the amount of monetary contribution.

Step 2: Determine the slope and y-intercept of the least squares regression line:
From the given information, we know that for every year increase since graduation, the contribution is expected to drop by $45. This gives us a slope of -45.

To find the y-intercept, we can use the mean values of X and Y. The mean of the number of years since graduation (X) is given as 5.5, and the mean of the amount of contribution (Y) is given as $132. We can substitute these values into the equation of a straight line (Y = mx + b) and solve for the y-intercept (b).

Using the values:
132 = -45 * 5.5 + b

Simplifying the equation:
132 = -247.5 + b

Adding 247.5 to both sides:
b = 132 + 247.5
b = 379.5

So, the y-intercept is 379.5.

Step 3: Use the regression line equation to predict the amount of contribution for an alumnus who graduated 5 years ago:
Substitute the value of X (number of years since graduation) as 5 into the equation of the regression line:
Y = -45 * 5 + 379.5

Calculating the equation:
Y = -225 + 379.5
Y = $154.50

Hence, the predicted amount of contribution made by an alumnus who graduated 5 years ago is $154.50.