chapter 1

Chapter 12: Simple Linear Regression and Correlation80. With sxygiven in the text,ˆβ1s=sxyxx. Also,sxyr = (where e.g.xx=s sSSE= n − 2: β ˆ1=xxyy∑s ( − x)x i2), and2 ˆ ˆˆs and SSE = Σyi− β0Σyi− β1Σxiyi= syy− β1sxy.Thus the t statistic for H 0 ist =s /s⋅∑βˆ1( x − x )in − 22o=( sxy/ sxx) ⋅ sxx2( s − s / s )/( n − 2)yyxy( s / s s )xxn − 2 r=sn − 2xyxy xx yy= =as desired.222( sxxsyy− sxy) 1−sxy/ sxxyy1−r81. Using the notation of the exercise above, syy2sxy2syy−2sxySSE s sxx xy= syy− , so 1−= 1−= = rs SST s s sxxyySST = and SSE = s yy− ˆβ1sxyxxyy2, as desired.82.a. A Scatter Plot suggests the linear model is appropriate.99.0removal%98.598.0510temp15389