Bivariate data obtained for the paired variables X and y are shown below, in the
ID: 3242179 • 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 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 y^.= 157.89 -1.41x In the "Calculations" table are calculations involving the observed y values, the mean y bar of these values, and the values y predicted from the regression equation. 1 For the data point (56.2, 762), 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 given by the which for these data is 3. The value r^2 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 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 which for these data isExplanation / Answer
We have given sample data of x and y.
We have given regression equation as,
y^ = 157.89 - 1.41*x
1.)
Residual = y - y^
where y^ is the predicted value of y.
We have to find residual for (56.2, 76.2)
First we find y^ at (56.2,76.2)
We can find y^ using regression equation.
y^ = 157.89 - 1.41*x
y^ = 157.89 - 1.41*56.2 = 78.65
Residual = 76.2 - 78.65 = -2.45
2. The vaiation in the sample y values that is not explained by the estimated linear relationship between x and y is given by the 1 - R^2.
where R is sample correlation between x and y.
R^2 is coefficient of determination.
For the given data sample correlation between x and y is denoted by r.
r = -0.9747
It indicates that there is negative relationship between x and y.
R^2 = -0.9747^2 = 0.9501
1 - R^2 = 1- 0.9501 = 0.0499
The vaiation in the sample y values that is not explained by the estimated linear relationship between x and y is 0.0499
3. The value r^2 is the proportion of the total variation in the sample y values that is explained by the estimated linear relationship between x and y.
r^2 = 0.9501
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 sum error squares which for these data is 19.5379.
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