Simple linear regression Explained and unexplained variation

Last updated: 6/28/2023

Simple linear regression Explained and unexplained variation 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 y 253 74 0 96x a 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 111 2 154 1 117 2 134 1 127 9 130 6 137 6 115 2 152 2 111 6 Send data to Excel Answer the following Calculations 5 624 0004 24 8004 2 1904 193 7664 306 9504 Column sum 1151 7080 50 5805 50 8084 0 1267 41 5251 15 7768 Column sum 158 8176 319 2654 146 6037 3 3709 55 8906 461 9061 Column sum 987 0366 100 IM in 13 130 DR Tin 13 EM 140 190 Figure 1 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 2 relationship between x and y For these data the value of 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 Att X G Espa ol