(Round all intermediate calculations to at least 4 decimal places.) Consider the
ID: 3365798 • Letter: #
Question
(Round all intermediate calculations to at least 4 decimal places.) Consider the following sample data (Use Table 2): x 13 2016 13 23 16 17 11 y 43 23 33 33 33 3134 33 Click here for the Excel Data File a. Find the sample regression line) = bo + b1X. (Negative values should be indicated by minus sign. Round your answers to 2 decimal places.) 43.080.63x b. Construct the 95% confidence interval for E(y) ifx = 15. (Round your answer to 2 decimal places.) to Confidence interval c. Construct the 95% prediction interval for y if x = 15. (Round your answer to 2 decimal places.) Prediction interval toExplanation / Answer
(a) here part (i) is correct.
(ii) 95% confidence interval for E(y) if x = 15
95% confidence interval = y^ +- tcrit * se
Here tcrit for dF = n -2 = 6 and alpha = 0.05
tcrit = 2.306
se = standard error = sxy sqrt [ 1/n + (x - x)2 /SSxx]
Here x = 15
x = 16.125 (Mean)
here Sxy = 5.1850 = STEYX(Rang of y, Range of x)
Sxx = 108.875 = DEVSQ(range of X)
these values one can calculate with the help of Excel.
here y^ (x = 15) = 43.08 - 0.63 x = 43.08 - 0.63 * 15 = 33.5867
95% confidence interval = y^ +- tcrit * se
= 33.5867 +- 2.306 * 5.1850 * sqrt [1/8 + (15 - 16.125)2 /108.875]
= 33.5867 +- 4.4195
= (29.1672, 38.0062)
= (29.17, 38.01)
(c) 95% predictioninterval for y if x = 15
95% prediction interval = y^ +- tcrit sxy sqrt [ 1 + 1/n + (x - x)2 /SSxx]
95% prediction interval = 33.5867 +- 2.306 * 5.1850 * sqrt [1 + 1/8 + (15 - 16.125)2 /108.875]
= 33.5867 - 12.7473
= (20.8394, 46.3340)
= (20.84, 46.33)
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.