Hours spent studying, x 1 1 3 3 4 6 Test score, y 38 44 50 47 64 70 Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (The pair of variables have a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The number of hours 6 students spent for a test and their scores on that test are shown below. (a) x = 2 hours (b) x = 4.5 hours (c) x = 12 hours (d) 1.5 hours Find the regression equation. Construct a scatter plot of the data and draw the regression line. (a) Now use the regression equation to predict the value of y for each of the given x-values, if meaningful. Because the correlation between x and y is significant, the equation of the regression line can be used to predict y-values. However, prediction values are meaningful only for x-values in the range of the data. Begin with x = 2. Since x = 2 is in the range of the original data it is meaningful to predict the value of y for x = 2. Now substitute 2 for x into the regression equation, then calculate ŷ, the predicted y-value. (b) Now predict the value of y for x = 4.5. Since x = 4.5 is in the range of the original data it is meaningful to predict the value of y for x = 4.5. (c) Next predict the value of y for x = 12. Since x = 12 is not in the range of the original data it is not meaningful to predict the value of y for x = 12. (d) Finally predict the value of y for x = 1.5. Since x = 1.5 is in the range of the original data it is meaningful to predict the value of y for x = 1.5
Hours spent studying, x | 1 | 1 | 3 | 3 | 4 | 6 |
Test score, y | 38 | 44 | 50 | 47 | 64 | 70 |
Find the equation of the regression line for the given data. Then construct a
(a) x = 2 hours (b) x = 4.5 hours (c) x = 12 hours (d) 1.5 hours
Find the regression equation.
Construct a scatter plot of the data and draw the regression line.
(a) Now use the regression equation to predict the value of y for each of the given x-values, if meaningful. Because the correlation between x and y is significant, the equation of the regression line can be used to predict y-values. However, prediction values are meaningful only for x-values in the
Begin with x = 2. Since x = 2 is in the range of the original data it is meaningful to predict the value of y for x = 2.
Now substitute 2 for x into the regression equation, then calculate ŷ, the predicted y-value.
(b) Now predict the value of y for x = 4.5. Since x = 4.5 is in the range of the original data it is meaningful to predict the value of y for x = 4.5.
(c) Next predict the value of y for x = 12. Since x = 12 is not in the range of the original data it is not meaningful to predict the value of y for x = 12.
(d) Finally predict the value of y for x = 1.5. Since x = 1.5 is in the range of the original data it is meaningful to predict the value of y for x = 1.5
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