Question

8.The following results were obtained from a survey carried out by professor Socrates The survey followed a strict and rigorous protocol in order to ensure as much as possible the reliability of the results. It involved a random sample of twenty eight engineering students registered in an advanced professionally related subject. The variable X represents the number of hours a student devoted to the study of the subject under consideration during the academic year while Y represents the marks out of hundred. rt X, 4,200.0 x 654,300.0 2Y -1,960.0; i-l ΣΥ,2-148,000.0 ΣΧΧ-307,284.0 n-28 ; ; is| (a) Compute the coefficient of correlation r of X and Y (b) Find the 95% confidence limits of the true coefficient of correlation . (c) Professor Socrates believed that Y and X are related by an equation of the form Y-fo + ßlX + e. where is a normally distributed random variable with mean equal to zero and unknown variance σ2. Write down the normal equations of the least squares line and then compute the estimates bo and bi of Po and respectively. (d) Sompute the error sum of squares and use this information to find the 95% onfidence limits of βι

Answer 1

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This page consists of answer to part a

Date nu limits n-3 28-3 1'156さ1.6 y 0.644> 0:9022 = Lorven Linnǐ七つ0.SH upper Limit0 022

This page contains the answer part b

Page No o.5 46 2.43 00 ○一(0546 x 150 Hence dt, 2 ESS- Sty-Sty 2 2 10800- 1328 243,00 ユー800-7261.92. ESS3538 08

This page contains the answer to part c . It also has the answer to the Error sum of square calculation part.

Page No Date TS: C" = ESS 538.08 2.8一2. 29-2 36.08 24300 0.5y6t 2 048 136.03 A24300 Lower Limit 039

This page contains the answer to the remaining (confidence limits) portion of part d.

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