Question

Please make the answer detailed and easy to read, thank you :)

B) Find the unexplained variation

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 Temperature 3 59 10 38 13 26 20 0 29 - 31 31 - 41 32 -55 a. Find the explained variation. (Round to two decimal places as needed.)

C) Find the indicated prediction interval

_____ degrees Fahrenheit < y < ______ degrees Fahrenheit

Answer 1

The statistical software output for this problem is :

Simple linear regression results: Dependent Variable: Temp Independent Variable: Altitude Temp = 73.817287 - 3.7733406 Altitude Sample size: 7 R(correlation coefficient) = -0.99505331 R-sq = 0.99013109 Estimate of error standard deviation: 4.7155136 Parameter estimates: Parameter Estimate Std. Err. DF 95% L. Limit 95% U. Limit Intercept 73.817287 3.7693141 5 64.127957 83.506616 Slope -3.7733406 0.16847261 5 -4.2064132 -3.340268 SS Analysis of variance table for regression model: Source DF MS F-stat P-value Model 1 11154.534 11154.534 501.64146 <0.0001 Error 5 111.18034 22.236069 6 11265.714 Total Predicted values: X value Pred. Y s.e.(Pred. y) 95% C.I. for mean 95% P.I. for new 6.327 49.943361 2.8746077 (42.553947, 57.332774) (35.74699, 64.139731)

Answers:

(a) 99.01 %

(b) 100-99.01 = 0.99 %

(c)  35.74699 <y< 64.139731