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Unformatted text preview: le 3 The following is a scatterplot of the final exam score versus midterm score for 11 sections of an introductory statistics class:#### ############Œ######0#####z###y## x## ###### ###$ŒÎv=ŒÎv=#########Œ##########z###,4# þ###Œ4#####$Ý4#ŒŒÎv= #.###The correlation coefficient for these data is #############Œ######2#####z###y## x## ###### ###$ŒÎv=ŒÎv=#########Œ##########z###,4# þ###Œ4#####$Ý4#ŒŒÎv= #à###. If you had a scatterplot of the final exam score versus midterm score for all individual students in this introductory statistics course, would the correlation coefficient be weaker, stronger, or about the same? Explain.###########Œ### ###4#####z###y## x## ###### ###$ŒÎv=ŒÎv=#########Œ#### #####z###,4# þ###Œ4#####$Ý4#ŒŒÎv= #####Relationships based on averages have a higher correlation coefficients than relationships based on individual data. Therefore, a scatterplot of the final exam score versus midterm score for the individual students would show much more scatter and a weaker correlation coefficient.##########Œ######6#####z###y## x## ###### ###$ŒÎv=ŒÎv=#########Œ############û#####z###,4# þ###"##########$Ý4#ŒŒÎv= #0###E#x#a#m#p#l#e# #4# #A# #r#e#s#i#d#u#a#l#s# #p#l#o#t# #o#f# #t#h#e# #r#e#s#i#d#u#a#l#s# #v#e#r#s#u#s# #t#h#e# #f#i#t#t#e#d# #v#a#l#u#e#s# #f#o#r# #r#e#c#o#r#d#-#b#r#e#a#k#i#n#g# #t#i#m#e#s# #o#f# #f#e#m#a#l#e# #m#a#r#a#t#h#o#n# #r#u#n#n#e#r#s# #f#o#r# #t#h#e# #y#e#a#r#s# #1#9#9#8# ## #2#0#0#3# #i#s#:####### ###Œ##############Œ######8#####z###y## x## ###### ###$ŒÎv=ŒÎv=#########Œ##########z###,4# þ###Œ4#####$Ý4#ŒŒÎv= ##### ##########Œ### ###:#####z###y## x## ###### ###$ŒÎv=ŒÎv=#########Œ##########z###,4# þ###Œ4#####$Ý4#ŒŒÎv= ##### ##########Œ### ###<#####z###y## x## ###### ###$ŒÎv=ŒÎv=#########Œ##########z###,4# þ###Œ4#####$Ý4#ŒŒÎv= #h###Based on this residuals plot, does it seem reasonable to use linear regression for this model? Explain.###########Œ######>#####z###y## x## ###### ###$ŒÎv=ŒÎv=#########Œ##########z###,4# þ###Œ4#####$Ý4#ŒŒÎv= ##### ##########Œ### ###@#####z###y## x## ###### ###$ŒÎv=ŒÎv=#########Œ#### #####z###,4# þ###Œ4#####$Ý4#ŒŒÎv= #v###Since we see clear pattern in the residuals plot, it does not seem reasonable to use linear regression for this model.#############Œ######B#####z###y## x## ###### ###$ŒÎv=ŒÎv=#########Œ##############z###,4# þ###"##########$Ý4#ŒŒÎv= #æ###E#x#a#m#p#l#e# #5# #H#e#r#e# #i#s# #a# #s#c#a#t#t#e#r#p#l#o#t# #o#f# #w#e#i#g#h#t# #v#e#r#s#u#s# #h#e#i#g#h#t# #f#o#r# #s#t#u#d#e#n#t#s# #i#n# #a#n# #i#n#t#r#o#d#u#c#t#o#r#y# #s#t#a#t#i#s#t#i#c#s# #c#l#a#s#s#.# # #T#h#e# #m#e#n# #a#r#e# #c#o#d#e#d# #a#s# ## 1## #a#n#d# #a#p#p#e#a#r# #a#s# #c#i#r#c#l#e#s# #i#n# #t#h#e# #s#c#a#t#t#e#r#p#l#o#t#;# #t#h#e# #w#o#m#e#n# #a#r#e# #c#o#d#e#s# #a#s# ## 2## #a#n#d# #a#p#p#e#a#r# #a#s# #s#q#u#a#r#e#s# #i#n# #t#h#e# #s#c#a#t#t#e#r#p#l#o#t#.####### ################Œ######D#####z###y## x## ###### ###$ŒÎv=ŒÎv=#########Œ##########z###,4# þ###Œ4#####$Ý4#ŒŒÎv= ##### ##########Œ### ###F#####z###y## x## ###### ###$ŒÎv=ŒÎv=#########Œ##########z###,4# þ###Œ4#####$Ý4#ŒŒÎv= #^###A) Do you think there is a clear pattern? Describe the association between weight and height.#############Œ######H#####z###y## x## ###### ###$ŒÎv=ŒÎv=#########Œ#### #########z###,4# þ###Œ4#########$Ý4#ŒŒÎv= #Œ###There is a moderately strong, positive association between weight and height. The variation in weight is larger for larger values of height.####Œ#################Œ######K#####z###y## x## ###### ###$ŒÎv=ŒÎv=#########Œ##########z###,4# þ###Œ4#####$Ý4#ŒŒÎv= ##### ##########Œ### ###M#####z###y## x## ###### ###$ŒÎv=ŒÎv=#########Œ##########z###,4# þ###Œ4#####$Ý4#ŒŒÎv= #H###B) Comment on any differences you see between men and women in the plot.###########Œ### ###O#####z###y## x## ###### ###$ŒÎv=ŒÎv=#########Œ#### #########z###,4# þ###Œ4#########$Ý4#ŒŒÎv= #Œ###Men, on average, appear to be taller and heavier than women. We can clearly see two groups (with some overlap) in tis scatterplot.####Œ###########Œ######Q#####z###y## x## ###### ###$ŒÎv=ŒÎv=#########Œ####I#####z###,4# þ###Œ4#####$Ý4#ŒŒÎv= ##### ##########Œ### ###S#####z###y## x## ###### ###$ŒÎv=ŒÎv=#########Œ##########z###,4# þ###Œ4#####$Ý4#ŒŒÎv= #Œ###C) Do you think a linear model from the set of all data could accurately predict the weight of a student with height 70 inches? Explain.##########Œ######U#####z###y## x## ###### ###$ŒÎv=ŒÎv=#########Œ#### ####### #########z###,4# þ###"##########$Ý4#ŒŒÎv= #N###S#i#n#c#e# #t#h#e#r#e# #a#p#p#e#a#r#s# #t#o# #b#e# #a# #d#i#f#f#e#r#e#n#c#e# #b#e#t#w#e#e#n# #m#e#n# #a#n#d# #w#o#m#e#n# #i#n# #t#h#e# #p#l#o#t#,# #i#t# #i#s# #n#o#t# #c#o#r#r#e#c#t# #t#o# #u#s#e# #a# #m#o#d#e#l# #o#b#t#a#i#n#e#d# #b#y# #t#h#e#s#e# #d#a#t#a# #t#o# #m#a#k#e# #a# #p#r#e#d#i#c#t#i#o#n#.# # #N#o#t#e# #t#h#a#t# #w#e# #c#a#n#n#o#t# #s#e#p#a#r#a#t#e# #t#h#e# #d#a#t#a# #i#n#t#o# #m#e#n# #a#n#d# #w#o#m#e#n# #t#o# #p#e#r#f#o#r#m# #s#e#p#a#r#a#t#e# #r#e#g#r#e#s#s#i...
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