Consider the following regression based on hypothetical data. Now we hypothesize
ID: 3224288 • Letter: C
Question
Consider the following regression based on hypothetical data. Now we hypothesize that only age and height affect people’s weight. So we run a regression analysis of data from a random sample of 25 people, with weight (in pounds) as the dependent variable and age (x variable 1, in years) and height (x variable 2, in inches) as the independent variables. Here is part of the regression output from Excel:
Coefficients
Standard Error
t Stat
P-value
Intercept
-44.67264562
50.1927185
-0.890022437
0.383084
X Variable 1
0.738473978
0.239186641
3.08743822
0.005381
X Variable 2
2.367599923
0.799362237
2.96186111
0.007203
One observation has age=20, height=65, and weight=130. What’s residual for this observation given the regression results?
Coefficients
Standard Error
t Stat
P-value
Intercept
-44.67264562
50.1927185
-0.890022437
0.383084
X Variable 1
0.738473978
0.239186641
3.08743822
0.005381
X Variable 2
2.367599923
0.799362237
2.96186111
0.007203
Explanation / Answer
Answer to the question)
From the regression analysis output we get to know that the Regression Equation is :
Weight = -44.6726 + 0.7385*Age +2.3656*Height
.
It is given that Age =20 & height = 65
for this the predicted Weight is as follows:
Weight = -44.6726 + 0.7385*20 +2.3656* 65
Weight = 123.8614
.
Weight (predicted) = 123.8614
Weight (observed) = 130
.
residual = Weight observed - weight predicted
residual = 130- 123.8614 = 6.1386
Thus the residual is between "0 and 25"