a) is given by the…regression sum of squares, error sum of squares, or total sum of squares these data is…1.8111, 17.2303, or 18.8080c) that minimizes the…regression sum of squares, error sum of squares, or total sum of squaresthese data is…1.8111, 17.2303, or 18.8080 **Answer the following:**(a) The variation in the sample $ y $-values that is explained by the estimated linear relationship between $ x $ and $ y $ is given by the (Choose one) ▼, which for these data is (Choose one) ▼.(b) 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 $ r^2 $ is [ ] (Round your answer to at least 2 decimal places.)(c) The least-squares regression line given above is said to be a line that "best fits" the sample data. The term "best fits" is used because the line has an equation that minimizes the (Choose one) ▼, which for these data is (Choose one) ▼. **Bivariate Data Analysis**Bivariate data obtained for the paired variables $ x $ and $ y $ are shown below in the table labeled "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 $ \hat{y} = 9.90 + 0.64x $.In the "Calculations" table are calculations involving the observed $ y $-values, the mean $ \bar{y} $ of these values, and the values $ \hat{y} $ predicted from the regression equation.### Sample Data| $ x $ | $ y $ ||---------|---------|| 22.3 | 24.1 || 23.5 | 25.3 || 26.6 | 25.7 || 27.8 | 28.1 || 30.3 | 29.4 |### Calculations| $ (y - \bar{y})^2 $ | $ (\hat{y} - \bar{y})^2 $ | $ (y - \hat{y})^2 $ ||-----------------------|-----------------------------|-----------------------|| 5.5131 | 0.0052 | 5.8564 || 2.4964 | 0.1269 | 1.4884 || 0.1632 | 1.4982 | 0.6724 || 1.3736 | 0.1665 | 2.4964 || 7.6840 | 0.0117 | 8.2944 |- **Column sum:** - $ (y - \bar{y})^2 $ = 17.2303 - $ (\hat{y} - \bar{y})^2 $ = 1.8111 - $ (y - \hat{y})^2 $ = 18.8080### Figure 1: Scatter PlotThe scatter plot displays the data points from the sample data (with $ x $-values on the horizontal axis and \( y \

Solution: Given information: SSR=∑(y^-y)2 SSR= 17.2303 Regression sum of squares SSE=∑(y-y^)2=1.8111 Error sum of squaresSST=∑(y-y)2 SST= 18.8080 Total sum of squares a) The variation in the sample y values that is explained by the estimated liner relationship between x and y is given by the regression sum of squares(SSR) which for these data is 17.2303 b) To find r2 r2=SSRSSTr2=17.230318.8080r2=0.92 The value r square is the proportion of total variation in the sample y values that is explained by the estimated linear relationship between x and y. For theses data the value of r square is 0.92 c) The least square regression line given above is said to be a line that best fits the sample data. The term best fits is used because the line has an equation that minimizes the error sum of squares (SSE) which for these data is 1.8111

Math

Statistics

Answer the following. (a) The variation in the sample y-values that is explained by the estimated linear relationship between x and y is given by the (Choose one) which for these data is (Choose one) (b) The value 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 r² is. (Round your answer to at least 2 decimal places.) (c) The least-squares regression line given above is said to be a line that "best fits" the sample data. The term "best 3

Answer the following. (a) The variation in the sample y-values that is explained by the estimated linear relationship between x and y is given by the (Choose one) which for these data is (Choose one) (b) The value 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 r² is. (Round your answer to at least 2 decimal places.) (c) The least-squares regression line given above is said to be a line that "best fits" the sample data. The term "best 3

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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