10.6 **Altitude and Temperature Analysis**Listed below are altitudes (in thousands of feet) and outside air temperatures (°F) recorded during a flight. The task is to find:1. **Explained Variation**2. **Unexplained Variation**3. **Indicated Prediction Interval**There is sufficient evidence to support the claim of a linear correlation. Therefore, it is reasonable to use the regression equation for predictions. For the prediction interval, use a 95% confidence level with an altitude of 6327 feet (or 6.327 thousand feet).**Data Table:**- **Altitude (thousands of feet):** 3, 6, 15, 22, 27, 31, 32- **Temperature (°F):** 57, 37, 23, 2, -27, -41, -57In this dataset, the relationship between increasing altitude and decreasing temperature can be analyzed using statistical methods to find variations and prediction intervals. ### Statistical Analysis Exercise**Tasks**a. Find the explained variation. [ ] (Round to two decimal places as needed.)b. Find the unexplained variation. [ ] (Round to five decimal places as needed.)c. Find the indicated prediction interval. [ ] °F < y < [ ] °F (Round to four decimal places as needed.)---*Note: Ensure that each calculated value is placed in the corresponding box, rounded to the specified number of decimal places.*

AltitudeTemperature357637152322227-2731-4132-57a)Use the given data to form the table: XYX*YX*XY*Y35717193249637222361369152334522552922244484427-27-72972972931-41-1271961168132-57-182410243249Sum136-6-3042346810810Determine the correlation coefficient using the formula:The explained variation for the given data set is 95.92%.b) The unexplained variation for the data set is 4.08%.c) The regression equation is given as .Determine the value of and :The regression equation is given as .The predicted temperature for the altitude of 6327 feet is .Use the excel formula, "=T.INV.2T(0.05,5)" for determining the critical value:tCritical = 2.5706Use the given data to form the table:XYX2Y^(Y−Y^)2357957.3510.1232016373646.72294.517284152322514.83566.667225222484-9.966143.18515627-27729-27.6810.46376131-41961-41.8530.72760932-571024-45.396134.652816Sum136-63468-5.988440.337052The prediction interval for estimated temperature is C.I = (17.52, 73.60).a) The explained variation for the given data set is 95.92%.b) The unexplained variation for the data set is 4.08%.c) The regression equation is given as .The prediction interval for estimated temperature is C.I = (17.52, 73.60).