Question

In the Fall STA 2023 Beginning of the Semester Survey, students were asked how many parties they attended every week and how many text messages they sent per day. The researcher decided to make the number of parties attended per week the explanatory variable and the number of text messages sent per day the response variable. The least squares regression line for this relationship is y-hat = 64.96 + 25.41x. One student attended 3 parties that week and sent 200 text messages per day. What is the residual?
A.58.81
B.-106.63
C.5146.96
D.4946.96
E.96.63
F.-96.63

Answer 1

Answer:

A.58.81

Step-by-step explanation:

x = number of parties attended

y = number of text messages sent

The residual is the difference between the actual number of text messages sent (200) and the number of texts predicted by the regression model:

$y=64.96+25.41x\\y=64.96+25.41*3\\y=141.19$

The residual is:

$R=200 - 141.19\\R=58.81$

The answer is alternative A.58.81