a) is given by the…total sum of squares, error sum of squares, or regression sum of squaresthese data is…838.9125, 1027.6120, or 187.4205c) that minimizes the…total sum of squares, error sum of squares, or regression sum of squaresthese data is…838.9125, 1027.6120, or 187.4205 ### Bivariate Data Analysis and Least-Squares Regression**Introduction**Bivariate data obtained for the paired variables \( x \) and \( y \) are shown in the "Sample data" table. These data are visualized in the scatter plot (Figure 1), which also displays the least-squares regression line. The equation of this line is \( \hat{y} = 257.91 - 1.00x \).**Sample Data**| \( x \) | \( y \) ||----------|----------|| 112.3 | 154.6 || 118.7 | 129.8 || 128.1 | 126.3 || 138.6 | 120.9 || 148.0 | 111.7 |**Calculations**Calculations are provided for the observed \( y \)-values, the mean \( \bar{y} \) of these values, and the values \( \hat{y} \) predicted from the regression equation.| \( (y - \bar{y})^2 \) | \( (\hat{y} - \bar{y})^2 \) | \( (y - \hat{y})^2 \) ||----------------------|-----------------------------|--------------------------|| 672.8836 | 80.8201 | 287.3025 || 1.2996 | 88.5481 | 111.3025 || 5.5696 | 12.3201 | 1.3225 || 60.2176 | 2.5281 | 87.4225 || 287.6416 | 3.2041 | 351.5625 || **Column sum:** 1027.6120 | **Column sum:** 187.4205 | **Column sum:** 838.9125 |**Scatter Plot and Regression Line (Figure 1)**- **Scatter plot**: The plot shows individual data points for the paired \( x \) and \( y \) values.- **Regression line**: A straight line representing the predicted relationship between \( x \) and \( y \) based on the least-squares method.The scatter plot demonstrates a negative linear relationship **Answer the following:**(a) The total variation in the sample \( y \)-values is given by the [Choose one], which for these data is [Choose one].(b) The proportion of the total variation in the sample \( y \)-values that can be explained by the estimated linear relationship between \( x \) and \( y \) 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].

Solution: Given information: SST=∑(y-y)2 SST= 1027.6120 Total sum of squares SSE=∑(y-y^)2 SSE=…

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 1, which also displays the least-squares regression line for the data. The equation for this line is y=257.91 -1.00x. - 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 112.3 154.6 118.7 129.8 128.1 126.3 138.6 120.9 148.0 111.7 Send data to Excel Calculations (x-1)² 672.8836 1.2996 5.5696 60.2176 287.6416 Column sum: 80.8201 88.5481 12.3201 2.5281 3.2041 Column sum: 287.3025 111.3025 1.3225 87.4225 351.5625 Column sum: 160- 150- 140- 130- 120+ 110. It 110 120 130 140 150 160

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 1, which also displays the least-squares regression line for the data. The equation for this line is y=257.91 -1.00x. - 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 112.3 154.6 118.7 129.8 128.1 126.3 138.6 120.9 148.0 111.7 Send data to Excel Calculations (x-1)² 672.8836 1.2996 5.5696 60.2176 287.6416 Column sum: 80.8201 88.5481 12.3201 2.5281 3.2041 Column sum: 287.3025 111.3025 1.3225 87.4225 351.5625 Column sum: 160- 150- 140- 130- 120+ 110. It 110 120 130 140 150 160

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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