Anything in blue should be done completed already. Struggling understanding the rest
Multiple Regression & ANOVA 1) Using Model 2 from the Coefficients table (Table 1.) below from today’s slides, please complete the following interpretations below for our regression coefficients for Sun and Advertising. Rainfall is already completed for you as an example. I have provided you with the actual tables below rather than snapshots of them in order to help you see them more clearly. Rainfall: b = 0.085 Mean Weekly Rainfall contributes significantly to our model (or significantly predicts our outcome variable), t = 12.261, p < .001.="" as="" mean="" weekly="" rainfall="" increases="" by="" one="" unit,="" umbrella="" sale="" numbers="" increase="" by="" 0.085="" units.="" both="" variables="" were="" measured="" in="" hundreds;="" therefore,="" for="" every="" 100="" more="" mm="" of="" rain,="" an="" extra="" 8.5="" umbrellas="" are="" sold.="" ="" sun:="" b="3.367" the="" mean="" weekly="" sun="" also="" contributes="" significantly="" at="" the="" 99%="" confidence="" level="" to="" umbrella="" sales="" with="" the="" p-value="" being="" p="">< .001="" (.000).="" what="" this="" tells="" us="" is="" that="" every="" week="" we="" have="" sunshine="" results="" in="" an="" extra="" 3.367="" umbrellas="" sold="" that="" week.="" advertising:="" b="11.086" the="" mean="" weekly="" advertising="" also="" contributes="" significantly="" at="" the="" 99%="" confidence="" level="" to="" umbrella="" sales="" with="" the="" p-value="" being="" p="">< .001="" (.000).="" what="" this="" tells="" us="" is="" that="" every="" week="" we="" place="" advertisements="" for="" umbrellas,="" the="" corresponding="" sales="" result="" in="" an="" extra="" 11.086="" umbrellas="" sold="" that="" week.="" table="" 1.="" coefficients="" unstandardized="" standardized="" bc="" 95%="" confidence="" interval="" coefficients="" coefficients="" b="" model="" b="" std.="" error="" beta="" t="" sig="" lower="" upper="" 1="" (constant)="" 134.140="" 7.537="" 17.799="" .000="" 119.278="" 149.002="" mean="" weekly="" rainfall="" (hundreds)="" .096="" .010="" .578="" 9.979="" .000="" .077="" .115="" 2="" (constant)="" -26.613="" 17.350="" -1.534="" .127="" -60.830="" 7.604="" mean="" weekly="" rainfall="" (hundreds)="" .085="" .007="" .511="" 12.261="" .000="" .071="" .099="" mean="" weekly="" sun="" 3.367="" .278="" .512="" 12.123="" .000="" 2.820="" 3.915="" mean="" weekly="" advertising="" 11.086="" 2.438="" .192="" 4.548="" .000="" 6.279="" 15.894="" dependent="" variable:="" umbrella="" sales="" (hundreds)="" 2)="" please="" use="" table="" 1.="" above="" again="" to="" complete="" the="" following="" interpretations="" below="" for="" our="" standardized="" regression="" coefficients="" for="" sun="" and="" advertising="" from="" model="" 2="" only.="" rainfall="" is="" already="" completed="" for="" you="" as="" an="" example="" ·="" rainfall:="" standardized="0.511" mean="" weekly="" rainfall="" contributes="" significantly="" to="" our="" model="" (or="" significantly="" predicts="" our="" outcome="" variable),="" t="12.261," p="">< .001.="" as="" average="" weekly="" rainfall="" increases="" by="" one="" standard="" deviation,="" umbrella="" sales="" increase="" by="" 0.511="" standard="" deviations.="" ·="" sun:="" standardized="0.512" mean="" sunshine="" also="" contributes="" significantly="" to="" the="" model="" of="" significantly="" predicting="" the="" outcome="" variable="" p="">< .001="" (.000="" significance).="" per="" one="" standard="" deviation="" of="" increased="" average="" sunshine="" per="" week,="" umbrella="" sales="" increase="" by="" 0.512="" standard="" deviation="" which="" is="" very="" much="" the="" same="" to="" additional="" increased="" weekly="" rainfall="" (0.511).="" ·="" advertising:="" standardized="0.192" similarly,="" mean="" advertising="" also="" contributes="" significantly="" to="" the="" model="" of="" significantly="" predicting="" the="" outcome="" variable="" p="">< .001 (.000 significance). per one standard deviation of increased advertisements per week, umbrella sales increase by 0.192 standard deviation. the contribution of increased advertisement yields less than both the increase rainfall and increased sunshine toward umbrella sales. 3) please respond to the following: a. why is adjusted r2 always smaller than r2? the adjusted r2 number is adjusted down from for the r2 number by subtracting the number of predictors in the model. b. the table below (table 2.) uses wherry’s formula to calculate adjusted r2. there issue with this because it is not provide a robust measure of adjusted r2. please use stein’s formula to calculate adjusted r2 from the r2 in the table below. stein’s formula: 1−[(?−1)(?−?−1)(?−2)(?−?−2)(?+1)?](1−?2) table 2. model summary model r r square adjusted r square std. error of est. r square change f change df 1 df 2 sig. f change 1 .578 .335 .331 65.991 .335 99.587 1 198 .000 2 .815 .665 .660 47.087 .330 96.447 2 196 .000 model 1 predictors: (constant), mean weekly rainfall (hundreds) model 2 predictors: (constant), mean weekly rainfall (hundreds), mean weekly sun, mean weekly advertising dependent variable: umbrella sales (hundreds) 4) please respond to the following questions regarding ssm and ssr: a. as discussed in class this week, in the anova situation, the ssm requires us to calculate the differences between each participant’s predicted value and the grand mean. what is each participant’s predicted value in anova? b. in the anova situation, ssm includes calculating the differences between what the model predicts and the grand mean. whereas ssr includes calculating the differences between what the model predicts and __________________ c. consider an independent anova situation with one iv that has three groups. let’s assume n=60 and participants are randomly assigned to each of the three groups with 20 individuals in each group. let’s assume the mean of the base group is 12.25, the mean of the low dose group is 14.28 and the mean of the high dose group is 17.43. let’s also assume that the grand mean is 15.36. please calculate the ssm for the anova situation. please make sure to show your work. d. in an anova situation, if our sst is 53.78 and our ssm is 34.12. what is the value of ssr. please show your work. 5) please respond to the following: a. using the regression equation to model an independent anova, the intercept (b0) is equal to what? b. using the regression equation to model an independent anova with 4-groups, the value of b1 is equal to what? .001="" (.000="" significance).="" per="" one="" standard="" deviation="" of="" increased="" advertisements="" per="" week,="" umbrella="" sales="" increase="" by="" 0.192="" standard="" deviation.="" the="" contribution="" of="" increased="" advertisement="" yields="" less="" than="" both="" the="" increase="" rainfall="" and="" increased="" sunshine="" toward="" umbrella="" sales.="" 3)="" please="" respond="" to="" the="" following:="" a.="" why="" is="" adjusted="" r2="" always="" smaller="" than="" r2?="" the="" adjusted="" r2="" number="" is="" adjusted="" down="" from="" for="" the="" r2="" number="" by="" subtracting="" the="" number="" of="" predictors="" in="" the="" model.="" b.="" the="" table="" below="" (table="" 2.)="" uses="" wherry’s="" formula="" to="" calculate="" adjusted="" r2.="" there="" issue="" with="" this="" because="" it="" is="" not="" provide="" a="" robust="" measure="" of="" adjusted="" r2.="" please="" use="" stein’s="" formula="" to="" calculate="" adjusted="" r2="" from="" the="" r2="" in="" the="" table="" below.="" stein’s="" formula:="" 1−[(?−1)(?−?−1)(?−2)(?−?−2)(?+1)?](1−?2)="" table="" 2.="" model="" summary="" model="" r="" r="" square="" adjusted="" r="" square="" std.="" error="" of="" est.="" r="" square="" change="" f="" change="" df="" 1="" df="" 2="" sig.="" f="" change="" 1="" .578="" .335="" .331="" 65.991="" .335="" 99.587="" 1="" 198="" .000="" 2="" .815="" .665="" .660="" 47.087="" .330="" 96.447="" 2="" 196="" .000="" model="" 1="" predictors:="" (constant),="" mean="" weekly="" rainfall="" (hundreds)="" model="" 2="" predictors:="" (constant),="" mean="" weekly="" rainfall="" (hundreds),="" mean="" weekly="" sun,="" mean="" weekly="" advertising="" dependent="" variable:="" umbrella="" sales="" (hundreds)="" 4)="" please="" respond="" to="" the="" following="" questions="" regarding="" ssm="" and="" ssr:="" a.="" as="" discussed="" in="" class="" this="" week,="" in="" the="" anova="" situation,="" the="" ssm="" requires="" us="" to="" calculate="" the="" differences="" between="" each="" participant’s="" predicted="" value="" and="" the="" grand="" mean.="" what="" is="" each="" participant’s="" predicted="" value="" in="" anova?="" b.="" in="" the="" anova="" situation,="" ssm="" includes="" calculating="" the="" differences="" between="" what="" the="" model="" predicts="" and="" the="" grand="" mean.="" whereas="" ssr="" includes="" calculating="" the="" differences="" between="" what="" the="" model="" predicts="" and="" __________________="" c.="" consider="" an="" independent="" anova="" situation="" with="" one="" iv="" that="" has="" three="" groups.="" let’s="" assume="" n="60" and="" participants="" are="" randomly="" assigned="" to="" each="" of="" the="" three="" groups="" with="" 20="" individuals="" in="" each="" group.="" let’s="" assume="" the="" mean="" of="" the="" base="" group="" is="" 12.25,="" the="" mean="" of="" the="" low="" dose="" group="" is="" 14.28="" and="" the="" mean="" of="" the="" high="" dose="" group="" is="" 17.43.="" let’s="" also="" assume="" that="" the="" grand="" mean="" is="" 15.36.="" please="" calculate="" the="" ssm="" for="" the="" anova="" situation.="" please="" make="" sure="" to="" show="" your="" work.="" d.="" in="" an="" anova="" situation,="" if="" our="" sst="" is="" 53.78="" and="" our="" ssm="" is="" 34.12.="" what="" is="" the="" value="" of="" ssr.="" please="" show="" your="" work.="" 5)="" please="" respond="" to="" the="" following:="" a.="" using="" the="" regression="" equation="" to="" model="" an="" independent="" anova,="" the="" intercept="" (b0)="" is="" equal="" to="" what?="" b.="" using="" the="" regression="" equation="" to="" model="" an="" independent="" anova="" with="" 4-groups,="" the="" value="" of="" b1="" is="" equal="" to="">