i. R-Square is the proportion of variance in the dependent variable (income) which can be predicted from the independent variable (food_exp). This value indicates that 38.5% of the variance in food_expcan be predicted from the variable income. j. Adjusted R-square. As predictors are added to the model, each predictor will explain some of the variance in the dependent variable simply due to chance. One could continue to add predictors to the model which would continue to improve the ability of the predictors to explain the dependent variable, although some of this increase in R-square would be simply due to chance variation in that particular sample. The adjusted R-square attempts to yield a more honest value to estimate the R-squared for the population. The value of R-square was .10, while the value of Adjusted R-square was .099. Adjusted R-squared is computed using the formula 1 - ( (1-R-sq)(N-1 / N - k - 1) ). From this formula, you can see that when the number of observations is small and the number of predictors is large, there will be a much greater difference between R-square and adjusted R-square (because the ratio of (N-1 / N - k - 1) will be much less than 1. By contrast, when the number of observations is very large compared to the number of predictors, the value of R-square and adjusted R-square will be much closer because the ratio of (N-1)/(N-k-1) will approach 1. k. This column shows the predictor variables below it (income). The last variable (_cons) represents the constant, or the Y intercept, the height of the regression line when it crosses the Y axis.

42 m. This column shows thedfassociated with the predictor. n. These are the values for the regression equation for predicting the dependent variable from the independent variable. The regression equation is presented in many different ways, for example... Ypredicted = b1+ b2*x1The column of estimates (coefficients or parameter estimates, from here on labeled coefficients) provides the values for b1 and b2 for this equation. Expressed in terms of the variables used in this example, the regression equation is Food_exppredicted = 83.416 + 10.210x incomeThese estimates tell you about the relationship between the independent variable and the dependent variable. This estimate indicates the amount of increase in food_expthat would be predicted by a 1 unit increase in the predictor, income. Note: If an independent variable is not significant, the coefficient is not significantly different from 0, which should be taken into account when interpreting the coefficient. (See the columns with the t value and p value about testing whether the coefficients are significant). income- The coefficient (parameter estimate) is 10.210. So, for every unit increase in income, a 10.210 unit increase in food expenditureis predicted.

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- Fall '19