Question

Fina cal ana st ?o that January credit card charges w geno a y be much k r than those o credit card charges of a random sample of 99 cardholders. Complete parts a) through e) below. he month before hat about the diff re co be woen January and the next month? ?? the trend continue? The accompanying data se contains the monthy Click the icon to view the monthly credit card charges. a) Build a regression medel to predict February charges from January charges. FebJar (Round to four decimal places as needed.) Check the conditions for this model. Select all of the true statements related to checking the conditions. A. All of the conditions are defintely satsfied. B. The Randomization Condition is not satisfied. C. The Nearly Normal Canctition is not satisfied D. The Linearity Condition is not satisfied E. The Equal Spread Condition is not satisfied. b) How much, on average, will cardholders who chargad $2000 in January charga in February? (Round to the nearest cent as needed.) c) Give a g5% confidence interval for the average February charges of cardholders wno charged $2000 in January. (Round to the nearest cent as needed.) d) From part c), givB a 95% confidence interval for the average derease in the charges of cardholders who charged $2000 in January. to the nearest cent as needed. e) What reservations, If any. would a researcher have about the contidence intervals made in parts c) and d)? Select all that apply. A. ? B. The data are not linear, so the confidence intervals are not valid. The data are not independent, so the confidence intervals are not valid. C- The residuals show a curvilinear pattern, so the confidence irttervals may not be valid. D. The residuals show increasing spread, so the confidence intervals may nat be vaid ?E. A researcher would not have any reservations. The confidence intervals are valid.

Answer 1

I have performed the linear regression programming in R

and here I get the model as follows

Feb=164.5127+0.7235*(Jan)

Call:
lm(formula = Y ~ X, data = Data)

Now for the question check all the conditions for model.Select the appropriate statements.

Coefficients:
(Intercept) X  
164.5127 0.7235

Now for the question "check all the conditions for model.Select the appropriate statements."

We check linearity by plotting observed value versus predicted value and it gives a plot which is linear.

rm(list=ls(all=TRUE))
Data=read.table("HomeworkLib.csv",header=TRUE,sep=',')
Data
lm(Y~X,data=Data)

f=function(x)
{
return(164.5127+(0.7235*x))
}
Y_hat=f(Data$Y);Y_hat

plot(Y_hat,Data$Y,type="l")

here is the code for checking linearity.

Randomisation is valid for multiple regression linear model.So this query does not count here.

To check the condition normality we perform normal quantile plot

Code:qqnorm(Data$Y)

The plot shows it is bow shaped.hence it is somewhat violate the normality assumption.

If we plot residuals we can see equally spread condition(homoscadiscity) is also satisfied.

Code:Res=resid(L)
Res
plot(Res,type='l')

for question b the cardholder has to pay 1611.513 for january.

question c and d is not valid because in question e b option is valid