Question

Attention: Due to 교 bug in Google Chrome, this page may not function correctly. Click her to learn more. 5. Comparing the fit of the regression lines for two sets of data Examine each of the following scatter diagrams and the corresponding regression lines. Identify which line better fits its data. Graph I Graph II 10 10 Next, calculate a measure of how close the data points are to the regression line. Following are the six pairs of data values for Graph I, along with the regression equation Yi 1.4 2.6 5.4 7.6 10 7.2 Y1.62 0.60x Calculabe the missing predicted values of y, residuals, and squared residuals to complete the following table. (Note: Your answers may differ slighty due to rounding. Select the responses that most closely match your results.) Data Values Predictedy Residual qed Residual Yi Vi (Y Y)2 2.6 2.82 -0.22 0.05 5.4 4.02 1.38 1.90 7.6 6.42 1.18 1.39 10 7.2 Calculabe the sum of the squares of the residual, the degrees of freedom, and the standard error of estimate for the data on Graph I. The SSE ,and the standard error of estimabe is The following are the six pairs of data values for Graph II, along with the regression equation Yi 0.2 2.6 4.6 3.2 10 8.6 y = 0.60x +0.71 Calculabe the missing predicted values of y, residuals, and squared residuals to complete the following table. Data Values Predictedy Residual Squared Residual yi 0.2 2.6 4.6 3.2 yi 1.91 0.69 0.48 4.31 1.11 1.23 5.51 -2.51 6.30 10 8.6 Calculabe the sum of the squares of the residual, the degrees of freedom, and the standard error of estimate for the data on Graph II. The SSE- and the standard error of estimabe is , At the beginning of the problem, you identified the data set whose regression line provided the better fit to its observations. Do the results of your calculations confirm your earlier answer? The standard error of estimate for Graph 1 İS of Graph II. Thus, the least squares line for Graph I fits its data You would expect the magnitude of the correlation coefficient for Graph I to be Graph IL. than that ne for Graph II fits its data. than the correlation coefficient for than the least squares li

Answer 1

Line in graph 1 fits the data better.

Degrees of freedom in both case is 4.

For Graph 1:

predicted y Residual 1.62 2.82 4.02 5.22 6.42 7.62 Squared Residual 0 2 4 0.22 0.22 1.38 1.62 1.18 0.42 0.0484 0.0484 1.9044 2.6244 1.3924 0.1764 6.1944 4 10 7.2 SUM 10 SSE Standard Error of Estimate- degree of freedom 6.1944 1.016 12 13 14

For Graph 2:

predicted y Residual 0.71 1.91 3.11 4.31 5.51 6.71 Squared Residual -0.51 0.69 1.49 1.11 2.51 1.89 0 0.2 0.2601 0.4761 2.2201 1.2321 6.3001 3.5721 14.0606 4 4 4.6 3.2 10 8.6 SUM 10 SSE Standard Error of Estimate- degree of freedom 14.0606 1.531 12 13

The standard error of estimate for graph 1 is smaller than that of graph 2. Thus the least squares line for graph 1 fits the data better than the least squares line for graph 2.

Correlation cofficient for graph 1 = 0.8968

Correlation cofficient for graph 2 = 0.7998

Correlation cofficient for graph 1 is greater than the Correlation cofficient for graph 2.

Yes results of calculations confirms our erlier answer that the line in graph 1 fits better than that of graph 2.

***************************************************