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# Statistics - Regression - Bivariate Data

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Bivariate data obtained for the paired variables x and y are shown below, in the table labelled "Sample Data". These data are plotted in the scatter plot (not shown), which also displays the least-squares regression line for the data. The equation for this line is ^y=1.86 + 0.48x.

In the "Calculations" table are calculations involving the observed y values, the mean -y of these values, and the values ^y predicted from the regression equation.

Sample Data
X Y
1.1 2.6
2.1 2.6
2.8 2.8
3.9 4.5
5.2 4.1

Calculations (y-^y)2 (^y--y)2 (y--y)2
0.0449 0.8686 0.5184
0.0718 0.2043 0.5184
0.1632 0.0135 0.2704
0.5898 0.1697 1.3924
0.0655 1.0733 0.6084
Column Sums 0.9353 2.3294 3.3080

1)For the data point (2.1,2.6) the value of the residual is ?. (Round your answer to at least 2 decimal places.)
2)The variation in the sample y values that is not explained by the estimated linear relationship between x and y is given by the a)error sum of squares, b)regression sum of squares, c)total sum of squares, which for these data is a)2.3294 b)3.3080 c)0.9353.
3)The value r squared is the proportion of the total variation in the sample y values that is explained by the estimated linear relationship between x and y. For these data, the value of r squared is ? (Round your answer to at least 2 decimal places.)
4)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 a)error sum of squares, b)regression sum of squares, c)total sum of squares, which for these data is a)2.3294 b)3.3080 c)0.9353.