Question

A marketing researcher studied annual sales of a product that had been introduced 10 years ago. The data are as follows, wher

hello

this is about linear regression

i want answer the question using R

write the results and command of R

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Answer #1

Answer -(a)-

here x taken as a dependent variable and y taken as a independent variable run the lm() function in R software for the simple linear regression .Below given the screen shot of R window and define command as well.

> x= c(0,1,2,3,4,5,6,7,8,9) > y= c(98, 135,162,178, 221, 232, 283, 300, 374, 395) > #Apply the lm () function for simple line

Hence using the output data fited model can formed as

y= 91.564 + 32.50x

ANS-(b)

Use the sqrt() command in R to transform the y variable like

> sqrt (y) [1] 9.899495 11.618950 12.727922 13.341664 14.866069 15.231546 16.822604 [8] 17.320508 19.339080 19.874607..................(step-1)(follow this step for other transformation like log(y)

then use the regression analysis process in the same manner

> print (summary (SLMM)) Call: lm (formula = sqrt(y) - x) Residuals: Min 10 Median 30 Max -0.47447 -0.30811 0.01549 0.29541 0

ANS (c)

when using y coeff of det. = 0.9798 and when taking square root of the y it becames 0.9891 much nearer to 1 since it can say after the transformation model is much precisesly predict the future values and model is good fit.

Ans(d)

put X=12 in each model

eg. in model two Y' = 10.26093+ 1.07629 * 12 =  23.17641

Y^1/2 = 23.17641

then Y = 537.146

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