SSxx= 135.115 SSxy=-706.269 SSyy=7510.962 xbar=2.708 ybar=76.9615 B1-5.2272 B0=91.23591) Test, at the 5% level of significance, the following hypotheses:Ho:B1=0 vs. H1:B1<02) Calculate a 95% confidence interval for B1 Correlation and regression analysis from start to finish:To investigate the relationship between class attendance and performance, an education re-searcher selects for study a multiple section introductory statistics course at a large university.Instructors agree to keep an accurate record of attendance throughout one semester. At theend of the semester 26 students are selected at random. For each student in the sample, twomeasurements are made: the number of days the student was absent (r) and the student's scoreon the common final exam (y). The data are summarized below:120764412963100964886398807919971896088196923904055190703688018420753806317846.800•...2.....x272 7270 0062 21 Processed data:Σx71Ey = 2001Ex? = 329Ery4758Ey161511

Solution: Given information: n= 26 SSxx= 135.115SSxy= -706.269SSyy= 7510.962x= 2.7308 y= 76.9615β1^= -5.2272β0^= 91.2359The sum of square of total SST is SST= SSyy= 7510.962 To find sum of square of regression SSR SSR = β1^×SSxy SSR= ( -5.2272)×(-706.269)SSR= 3691.809316SSR= 3691.8093 To find sum of square of error = SSE SST= SSR + SSE SSE = SST - SSR SSE = 7510.962 - 3691.8093 SSE= 3819.1527 To find Standard error of the slope coefficient S.E( β1^)= SSE(n-2)×SSxxS.E( β1^)= 3819.152724×135.115S.E( β1^)= 3819.15273242.76S.E( β1^)= 1.177748S.E( β1^)= 1.0852 1) To test the hypothesis Ho: β1=0 VS Ha:β1<0 Test statistic t= β1^S.E(β1^)t= -5.22721.0852= -4.816808t= -4.8168 Test statistic t= -4.8168 To find p value p value = P( t< -4.8168) p value = 0.0000 From Excel Decision: p value < α=0.05. Reject the null hypothesis Conclusion: There is sufficient evidence to conclude that β1 is negative . ( β1 <0) 2) The 95% confidence interval for the slope β1 is β1^±tα/2,n-2×S.E( β1^)At α=0.05tα/2,n-2 =t0.025, 24= 2.064 From t table ( -5.2272±2.064×1.0852)(-5.2272±2.239853)(-5.2272-2.239853, -5.2272+2.239853)(-7.467053, -2.987347)(-7.4671, -2.9873) The 95% confidence interval for the slope β1 is ( -7.4671, -2.9873)

Math

Statistics

SSxx= 135.115 SSxy=-706.269 SSyy=7510.962 xbar=2.708 ybar=76.9615 B1-5.2272 B0=91.2359 1) Test, at the 5% level of significance, the following hypotheses: Ho:B1=0 vs. H1:B1<0 2) Calculate a 95% confidence interval for B1

SSxx= 135.115 SSxy=-706.269 SSyy=7510.962 xbar=2.708 ybar=76.9615 B1-5.2272 B0=91.2359 1) Test, at the 5% level of significance, the following hypotheses: Ho:B1=0 vs. H1:B1<0 2) Calculate a 95% confidence interval for B1

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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