Athletes are constantly seeking measures of the degree of their cardiovascular fitness prior toa major race. Athletes want to know when their training is at a level which will produce apeak performance. One such measure of fitness is the time to exhaustion from running on atreadmill at a specified angle and speed. The important question is then "Does this measureof cardiovascular fitness translate into performance in a 10-km running race?" Twentyexperienced distance runners who professed to be at top condition were evaluated on thetreadmill and then had their times recorded in a 10-km race. The data are given here.a.b.C.d.Treadmill Time (minutes) 7.5 7.8 7.9 8.1 8.3 8.7 8.9 9.2 9.410-km Time (minutes) 43.5 45.2 44.9 41.1 43.8 44.4 42.7 43.1 41.8Treadmill Time (minutes) 10.1 10.3 10.5 10.7 10.8 10.9 11.2 11.510-km Time (minutes) 39.5 38.2 43.9 37.1 37.7 39.2 35.7 37.2 34.8 38.511.7 11.89.843.7Construct the scatter plot to see the appropriateness of a linear model and comment on it?Obtain the estimated linear regression model ŷ = ₁ + ₁xXEstimate oz.Find the standard error of B₁.

It is required to obtain a scatter plot to assess the appropriateness of a linear model, fit the linear regression model, find the quantity σε2, and also find the standard error of the estimated slope.a.Denote the dependent variable, “10-km Time (minutes)” as y, and the independent variable, “Treadmill Time (minutes)” as x.We have used Excel for the scatterplot and regression analysis. The data is:Select the cells A1 to B21.Go to Insert, choose Insert (X, Y) or Bubble Chart, and select Scatter.Go to Design, choose Quick Layout, and select a layout with chart title and axes titles; edit the titles.Double-click on the horizontal axis ticks, and set the minimum bound to 7 (as the minimum value of the Treadmill Time (minutes) is 7.5), and the maximum bound to 12 (as the minimum value of the Treadmill Time (minutes) is 11.8).Double-click on the vertical axis ticks, and set the minimum bound to 34 (as the minimum value of the 10-km Time (minutes) is 34.8).The scatter plot obtained is:The graph shows that the points form a gradually decreasing pattern, with the highest 10-km times corresponding to the lowest treadmill times, and the lowest 10-km times corresponding to the highest treadmill times, in general. There is no clear curvature formed by the plotted points, and they lie, more-or-less, in a band of constant width. Although the points do not lie on a perfect straight line, they are quite tightly clustered around an imaginary straight line, in a linear manner.Thus, a linear model would be appropriate to fit in this data.b.The estimated model is of the form: , where is the estimated intercept, and is the estimated slope.To obtain the linear regression model, go to Data, select Data Analysis and choose Regression.In Input Y Range, select $B$1:$B$21.In Input X Range, select $A$1:$A$21.Select Labels, click OK.The regression output is:Using the values from the “Coefficients” column in the output, the linear regression model is:c.The quantity σε2 is the mean square error estimated from the model.From the row “Residual” for error and column “MS” for mean square, the estimated value of σε2 is 3.729997814.d.The required standard error is the standard error for the estimated slope.From the row “x” and column “Standard Error”, the standard error for the estimated slope is 0.318154807.a. The scatter plot is: A linear model is appropriate.b. The estimated linear regression model is: .c. The estimated value of σε2 is 3.729997814.d. The standard error for is 0.318154807.