10.16 Listed below are altitudes (thousands of feet) and outside air temperatures (°F)recorded during a flight. Find the (a) explained variation, (b) unexplained variation,and (c) indicated prediction interval. There is sufficient evidence to support a claim ofa linear correlation, so it is reasonable to use the regression equation when makingpredictions. For the prediction interval, use a 95% confidence level with the altitudeof 6327 ft (or 6.327 thousand feet).AltitudeTemperature+357637152322227- 2731- 4132- 57-

To find the explained variation, need to compute the Coefficient of Determination (R2 )The following data for the X and Y variables are provided to find the sample correlation coefficient:xy357637152322227-2731-4132-57xyx*yx^2y^235717193249637222361369152334522552922244484427-27-72972972931-41-1271961168132-57-182410243249Total136-6-3042346810810Based on the above table, the following is calculated: Therefore, The coefficient of Determination = R2 = -0.9794*-0.9794 = 0.9592The model explains 95.92% of the variation in the data i.e. Explained variation = 0.9592b)The unexplained variation is c) Indicated production interval 95% Production interval for y at =6.327a) Explained variation = 0.9592b) unexplained variation =0.0408c) Indicated production interval =45.5605