For each of the sums of squares in regression, state its name and what it measures,
a) SST measures how much variation is there in the observed data.
b) SSR measures the variation in the modeling errors.
c) SSE (Sum of squares Error) is the difference between the observed value and the predicted value.
To determine the name of SST and to explain what it measures.
The regression sum of squares is obtained by dividing the corresponding sum of squares by the degrees of freedom. In regression, whether the terms in the model are significant or not is determined by using the mean squares. The mean square is the term obtained by dividing the sum of squares by the degrees of freedom.
SST (Sum of Squares Total) is the squared difference between the observed dependent variable and its mean.
To determine the name of SSR and to explain what it measures.
S S R (Sum of Squares due to Regression) is the sum of the differences between the predicted value and the mean of the dependent variable.
To determine the name of S S E and to explain what it measures.
SSE measures how much variation is there in the modeled values and this is compared to the total sum of squares and to the residual sum of squares.
4.78 Gas Guzzlers. The magazine Consumer Reports publishes information on automobile gas mileage and variables that affect gas mileage. In one issue, data on gas mileage (in miles per gallon) and engine displacement (in liters) were published for vehicles. Those data are available on the Weiss Stats site.
a. Obtain a scatterplot for the data.
b. Decide whether finding a regression line for the data is reasonable. If so, then also do parts (c) (f).
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