Data Description: US macro data on monthly real disposable personal income

$($DSPIC$96),$ real personal consumption expenditures $($PCEC$96),$ and $5-$year Treasury

interest rates $($GS$5).$

This homework has two parts:

I. Prepare these data in Excel for use in the statistical software R$.$Once you import the data to R$,$ check your data with head$()$ and tail$()$ function so that you are sure your data is correct. Explore the data and report summarize statistics.

II$.$ Run the regression program of a simple consumption model described below. The basic consumption function model says that consumption is explained by disposable income. Be sure to set up the dependent variable to reflect this model and use R to generate a table reporting all regression results.

Based on your data results, answer the following questions $($Also submit your R file along with associated Excel data$)$:

$1.$ Write a simple consumption model by clearly stating dependent variable and independent variable.

$2.$ Describe the OLS methodology based on your model. Setup the objective function, and indicate the decision variables.

$3.$ Look at descriptive statistics of your data using summary$()$ function and using stargazer$()$ to generate a nice Table $($call it Table $1).$ Comments on the results $($e$.$g$.,$ n$,$ mean, standard deviation, min and max$).$

$4.$ Plot dependent variable and independent variable over time. Comment on your plot.

$5.$ Often time, we compare annual consumption$/$income year to year. Report the summarized statistics by year.

Try sample code below:

mydata$year$<-$substr$($mydata$Date,$1,4)$

tapply$($mydata$PCEC$96,$ mydata$year, mean$)$

tapply$($mydata$DSPIC$96,$ mydata$year, mean$)$

tapply$($mydata$GS$5,$ mydata$year, mean$)$

$6.$ Now run OLS model $($call Model$1)$ and write out the estimated regression model.$$ How do you interpret the intercept and slope values of the model? Be sure to comment on the sign, magnitude and significance of the slope value.

$7.$ Use the equation to predict the dependent value, given a value of the independent variable of $$8200$ Billion.

$8.$ What is the R$-$squared? What does R$-$squared mean in general and what does this value tell us$?$

$9.$ What is the F$-$Value? What does F mean in general and what does this particular value of F tell us$?$ This is all the information I have