### Regression Analysis of Ice Hockey Team PerformanceThe table below displays the data for the number of goals allowed and the corresponding total points earned by 14 ice hockey teams over the course of a season. Points are calculated with 2 points for a win and 1 point for an overtime or shootout loss. The regression equation provided for this dataset is $ \hat{y} = -0.615x + 228.937 $.#### Data Table:| Goals Allowed, $ x $ | 213 | 205 | 217 | 226 | 252 | 257 | 277 | 197 | 217 | 198 | 220 | 205 | 255 | 245 ||------------------------|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|| Points, $ y $ | 110 | 102 | 100 | 96 | 89 | 76 | 45 | 106 | 101 | 101 | 97 | 85 | 73 | 66 |#### Tasks:(a) Find the coefficient of determination, $ r^2 $, and interpret the result.(b) Find the standard error of the estimate, $ s_e $, and interpret the result.##### Explanation:**(a) Coefficient of Determination, $ r^2 $:**\[ r^2 = \_\_\_ \](Round to three decimal places as needed.)**(b) Standard Error of the Estimate, $ s_e $:**\[s_e = \_\_\_\]The coefficient of determination $ r^2 $ indicates how well the regression line approximates the real data points. It measures the proportion of the variance in the dependent variable (points, $ y $) that is predictable from the independent variable (goals allowed, $ x $). The standard error of the estimate $ s_e $ represents the average distance that the observed values fall from the regression line. Both these metrics provide insight into the accuracy and reliability of the regression model used for predictive purposes.

We have to calculate coefficient of determination and standard error

Answered: The table shows the number of goals…

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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The table shows the number of goals allowed and the total points earned (2 points for a win, and 1 point for an overtime or shootout loss) by 14 ice hockey teams over the course of a season. The equation of the regression line is ŷ= -0.556x+217.766. Use the data to answer the following questions. (a) Find the coefficient of determination, 12, and interpret the result. (b) Find the standard error of the estimate, Se, and interpret the result. 213 213 223 226 259 266 281 202 210 205 226 207 259 239 D Goals Allowed, x Points, y 109 109 102 91 88 80 52 105 107 98 95 85 68 66 (a)² = (Round to three decimal places as needed.) Interpret the coefficient of determination. Select the correct choice below and fill in the answer box to complete your choice. (Round to one decimal place as needed.) OA. About OB. About (b) Se = % of the variation in points earned can be explained by the relationship between number of goals allowed and points earned. The remaining variation is unexplained. % of the…
The table shows the average weekly wages (in dollars) for state government employees and federal government employees for 8 years. The equation of the regression line is y=1.410x−17.174. Complete parts (a) and(b) below.

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