Question

6 of 6 (6 complete) HW Score: 83.33%, 5 of 6 pts Score: 0 of 1 pt X 10.3.17-T Question Help 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 of a linear correlation, so it is reasonable to use the regression equation when making predictions. For the prediction interval, use a 95% confidence level with the altitude of 6327 ft (or 6.327 thousand feet). Altitude 8 15 23 29 31 33 0 Temperature T 56 34 26 -5 -25 -41 -57 a. Find the explained variation (Round to two decimal places as needed.) Enter your answer in the answer box and then click Check Answer wer 2 parts 2 remaining Clear All Check Answer vºzy 1st Edition View all solutions 20%
a. find the explained variation

b.find the unexplained variation

c.find the indicated prediction interval

Answer 1

Consider altitude be the independent variable, x and temperature be the dependent variable, y. Minitab is used to analyze the provided data. Steps are as: 1. Enter the data into the worksheet. 2. Go to Stat>Regression>Regression>Fit Regression Model. 3. Select "Temperature" in Responses and "Altitude" in Continuous Predictors. 4. Click Results>Expanded Tables>ok twice. 5. The result is obtained as:

Regression Equation Temperature = 68.98 - 3.485 Altitude Coefficients Coef SE Coef T-Value P-Value Term 95% CI VIF 68.98 6.72 (51.72, 86.25) 0.291 (-4.234, -2.736) Constant 10.27 0.000 -3.485 Altitude -11.96 0.000 1.00 Model Summary PRESS R-sq(pred) BIC R-sq R-sq(adj) 61.36 8.43498 96.62% 95.94% 681.709 93.52% 53.20 Analysis of Variance Adj sS Adj MS Seq ss Contribution 1 10171.7 F-Value P-Value Source DF 142.96 Regression 96.62% 10171.7 10171.7 0.000 Altitude 10171.7 96.62% 10171.7 10171.7 142.96 0.000 Error 355.7 3.38% 355.7 71.1 Total 10527.4 100.00% (a) From the obtained output, the explained variation is, SSR = E(-y) = 10171.7 %3D

(b) From the obtained output, the unexplained variation is, SSE = E(y-i) = 355.7 (c) The 95% prediction interval when altitude is 6.327 thousand ft. is, 1. Enter the data into the worksheet. 2. Go to Stat>Regression>Regression>Predict. 3. Select "Temperature" in Responses and enter 6.327 in “Altitude". 4. Click Ok. 5. The result is obtained as:

Regression Equation Temperature 68.98 - 3.485 Altitude !! Settings Variable Setting Altitude 6.327 Prediction Fit SE Fit 95% CI 95% PI 46.9340 5.16899 (33.6467, 60.2213) (21.5038, 72.3643) From the above output, the 95% prediction interval is obtained as (21.5038, 72.3643).