Consider the following regression based on hypothetical data. We hypothesize tha
ID: 3224006 • Letter: C
Question
Consider the following regression based on hypothetical data. We hypothesize that age, height, and income 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), height (x variable 2, in inches), and income (x variable 3, in $1,000) as the independent variables. Here is part of the regression output from Excel:
2. With the observation of age=20, height=65, and weight=130, what's the aproximate predicted weight given the regression results? What's the residual?
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 0.007203Explanation / Answer
The fitted regression model is
weight= -44.67 + 0.74 (age)+ 2.37 (height)
With the observation of age=20, height=65
weight= -44.67 + 0.74 (20)+ 2.37 (65) =124.18
Residual= actual - fitted =130-124.18 = - 5.82