Bivariate data obtained for the paired variables x and y are shown below, in the
ID: 3324968 • Letter: B
Question
Bivariate data obtained for the paired variables x and y are shown below, in the table labelled "Sample data." These data are scatter plot in Figure 1, which also displays the least-squares regression line for the data. The equation for this line is 242.10-0.86x le are calculations involving the observed y values, the mean y ot these values, and the values predicted y values, the mean y of these values, and the values mean y of t from the regression equation. Sample data Calculations vmy 23.1169368 3329 107,8 154.2 117.6 134.3 1322 125.6 1422 120.5 147.4 116.4 576.0000 115.8637 '20 16.8100 21.1600 94.0900 190.4400 7.8849 04789 1.1321220.9385 3.2113 |column!. 898 5000-770216 816.3400 110150 13140 150 160 Figure 1 Answer the following: 1. For the deta point (117 6, 134.3), the value of the tesidual is . Round your answer to at least 2 decimal places.) 2. The least-squares regression line givon above is said to be a line which "bes: fits" the sample data. The term "best fits" is used because the line has an equation that minimizes the D. which for these data is (2 .which for 3. The total variation nne sample yvaues isguen by the these data is (2. 4The proportion of the total variation in the sample y values that can be explained by the estimated iinear relationship between x and y is 1·(Round your answer to at least 2 decimal paces)Explanation / Answer
1.
The regression line is y = 242.10 - 0.86 x
For x = 117.6
y = 242.10 - 0.86*117.6 = 140.964
Residual = observed - predicted = 134.3 - 140.964 = -6.664
2.
error sum of squares
From the data,
SSE = 77.0216
3.
total sum of squares
From the data,
SST = 898.5
4.
From the data,
SSR = 816.34
r2 = SSR / SST = 816.34/898.5 = 0.9086
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.