The utility bills (in dollars) for homes is estimated by a multiple regression e
ID: 3300172 • Letter: T
Question
The utility bills (in dollars) for homes is estimated by a multiple regression equation using the independent variables X1 (the number of occupants) and X2 (the number of rooms) in the home. The regression equation is given below: y(hat) = 300 + 7 X1 + 13 X2
a. Identify the y- intercept and the partial slopes of this model.
b. Interpret the meaning of they-intercept and the partial slopes with reference to the context.
c. What is the predicted bill for a family of 5 that lives in a 6-room home? According to the data, the bill was $399.00. What is the residual?
d. Another researcher used a different number of variables and tried to predict a more reliable model. In the analysis he noticed that a couple of partial regression coefficients exhibited the wrong sign. What potential problem does this indicator suggest? Explain the problem.
e. What is stepwise regression, and when is it desirable to make use of this particular multiple regression technique?
f. Data from a different study indicated that the SS Residual (SS Error) is 150. If the researcher had fitted a regression equation model with 25 observations and had used 6 independent variables, what is the standard error of the estimate (model standard deviation)? What is the relevance of this measure in statistical analysis?
Explanation / Answer
SOL:
y(hat) = 300 + 7 X1 + 13 X2
y intercept=300
slope of X1=7
slope of X2=13
Solutionb;
for slope x1=7 intrepretation is
if x2 is fixed,then for each change of 1 unit in x1 ,y changes 7 units
for slope x2=13 the intrepretation is,
if x1 is fixed,then for each change of 1 unit in x2, y changes 13 units
y intercept=300 means as the value you predict for y if both x1=0 and x2=0
Solutionc:
x1=5 x2=6
y(hat) = 300 + 7 X1 + 13 X2
substitute in regresison eq
y(hat) = 300 + 7 (5) + 13 (6)
=413
residual=actual -redicted
=399-413
=-14
Solutione:
This form of regression is used when we deal with multiple independent variables. In this technique, the selection of independent variables is done with the help of an automatic process, which involves no human intervention.
This feat is achieved by observing statistical values like R-square, t-stats and AIC metric to discern significant variables. Stepwise regression basically fits the regression model by adding/dropping co-variates one at a time based on a specified criterion. Some of the most commonly used Stepwise regression methods are listed below:
The aim of this modeling technique is to maximize the prediction power with minimum number of predictor variables. It is one of the method to handle higher dimensionality of data set.
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