Question

(a) 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 7, and the amount of contribution has a mean of 195 dollars. 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 37 dollars. Predict the amount of contribution made by an alumnus who graduated 4 years ago. Do not round in intermediate steps. The predicted contribution of an alumnus who graduated 4 years ago is: (in dollars, rounded to one decimal place.) (b) An analyst working for a telecommunications company has been asked to gauge the stress on its cellular networks due to the increasing use of smartphones. She decides to first look at the relationship between the number of minutes customers spent talking on their phones and the amount of cellular data they use. She collects a month's worth of data on 300 customers who have smartphones with data plans. The mean monthly call time was found to be 286 minutes, and the mean amount of data consumed was found to be 578 megabytes. Based on the least squares regression line fitted to the data, it is found that for every minute increase in calling time, the data usage is expected to increase by 3.8 megabytes. Predict the amount of data used by a customer who spends 423 minutes on the phone. Do not round in intermediate steps. (in megabytes, The predicted the amount of data used by a customer who spends 423 minutes on the phone is: rounded to one decimal place).

Answer 1

Solution:

(a) x-bar = 7
y-bar = 195
b1 = -37

b0 = 195-(-37*7)= 454

The predicted of an alumnus who graduated 4 years ago is:
x = 4
y-hat = 454 - 37*4 = 306
contribution amount= $306
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(b) Here we have
y_hat(x)=Ax+B
where
A= 3.8
B is obtained from solving
578 = 3.8(286)+B
from which B= -508.8
Hence
y_hat(x) = 3.8x-508.8

Predict the amount of data used by a customer who spends 423 minutes on the phone

y_hat(423) = 3.8(423)-508.8 = 1098.6 Mb