Explained and unexplained variation and the least-squares regression line
Bivariate data obtained for the paired variables and are shown below, in the table labelled "Sample data." These data are plotted in the scatter plot in Figure 1, which also displays the least-squares regression line for the data. The equation for this line is.
In the "Calculations" table are calculations involving the observed values, the mean of these values, and the values predicted from the regression equation. y=60.11+.58x
- ^ - ^
x y y-y2 y-y2 y-y2
111.2 125.3 87.9844, 104.4855 - 0.4816
118.4 131.8 8.2944, 34.7864 - 9.1083
131.2 123.6 122.7664, 2.3287- 158.9122
137.1 146 128.1424, 24.4827- 40.60241
147.6 146.7 144.4804, 121.8374- 0.9643
sums 491.668, 284.9207- 210.0679
1. The least squares regression line given above is said to be a line which best fits the sample data. The term 'best fits' is used because the line has an equation that minimizes the _________?which for these data is ________?
2. For the data point 118.4,131.8, the value of the residual is_________?
3. The total variation of the sample y value is given by the ________? which for these data is _____________?
4. The proportion of the total variation in the sample y values that can be explained by the estimated linear realtionship between x and y is___________________?
Step by step method for computing regression model for a given data set.