A sample of 25 families was taken for a study. The objective of the study was to estimate the factors that determine the monthly expenditure (in dollars) on food for families. The independent variables included in the analysis were the number of members in the family (x1), the number of meals eaten outside (x2), and a dummy variable (x3) that equals 1 if a family member is on a diet and equals 0 if there is
A sample of 25 families was taken for a study. The objective of the study was to estimate the factors that determine the monthly expenditure (in dollars) on food for families. The independent variables included in the analysis were the number of members in the family (x1), the number of meals eaten outside (x2), and a dummy variable (x3) that equals 1 if a family member is on a diet and equals 0 if there is no family member on a diet. The following regression results were obtained
|
|
Coefficients |
Standard Error |
|
Intercept |
450.08 |
53.6 |
|
x1 |
49.92 |
9.6 |
|
x2 |
10.12 |
2.2 |
|
x3 |
-.60 |
12.0 |
- What are the degrees of freedom for the sum of squares explained by the regression (SSR) and the sum of squares due to error (SSE)?
- Test whether or not there is a significant relationship between the monthly expenditure on food and the independent variables. Use a .01 level of significance. Be sure to state the null and alternative hypotheses.
- Compute the multiple coefficient of determination and explain its meaning.
- Estimate the monthly expenditure on food for a family that has 4 members, eats out 3 times, and does not have any member of the family on a diet.
Multiple linear regression model:
A multiple linear regression model is given as y = b0 + b1x1 + b2x2 + u where y is the predicted value of response variable, and x1, x2 are the predictor variables. The quantities b1, b2 are the estimated slopes corresponding to x1, x2 respectively and b0 is the estimated intercept of the line, from the sample data.
A multiple regression equation describes the combined effect of all the predictors in the model. Even when the effect of a particular predictor is being studied from a multiple regression equation, it assumes that the effects of all the other predictors are accounted for.
Here, the dependent variable is monthly expenditure and the independent variables are number of members in the family, number of meals eaten outside, dummy variable.
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