Question

Simple Linear Regression Problem

Simple Linear Regression Problem

QUESTION 4 SUMMARY OUTPUT Regression Statistics Multiple R Squared Adjusted Rsq Standard Error Observations 0.90 0.80 0.79 82.06 19.00 ANOVA MS 467247.5 6733.3 df Regression Residual Total 467247.5 114466.2 581713.7 17 Intercept Age Coefficients St Error 756.26 10.27 30.41 1.23 t Stat 24.87 -8.33 This output was obtained from data on the age of houses (in years) and the associated amount paid in rates (S). Predict the rates paid (in dollars correct to two decimal places) for a house that is 40.7 years old

Answer 1

Solution:

From the given output, we have:

$\dpi{100} \large intercept=756.26$

$\dpi{100} \large Slope=-10.27$

Therefore, the least squares regression equation is:

$\dpi{100} \large \boldsymbol{\hat{y}=756.26+(-10.27)Age}$

We are given, the $\dpi{100} \small Age=40.7$ , therefore, the rates paid (in dollars) using the above least squares regression equation is:

$\dpi{100} \hat{y}=756.26+(-10.27) \times 40.7$

  $\dpi{100} =338.27$

Therefore, the predicted rates paid (in dollars) is $\dpi{100} \boldsymbol{338.27}$