Homework #$6$ Assignment: A project on SLR

We will use the computer software to gather data and estimate equations in class for this

data$-$based homework.

This homework has three parts:

I. Use the web to get US macro data on monthly real disposable personal income

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

interest rates $($GS$5).$

II$.$ 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.

III. 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 $($at

least describe mean, variance, min and max$).$

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

plot.

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

summarize statistics by year $($include answers in R code$).$

$6.$ Now run OLS model $($call Model$1)$ and write out the resulting equation

$($regression line$).$ How do you interpret the intercept and slope values of the

regression line? $($Do not worry if the intercept is not a reasonable data point for

consumption because we do not have any data that is close to the intercept

values$).$ Be sure to comment on 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$?$

Finally, one student wonders what would happen if we regress the logs of the

variables in the above basic equation $($Model$1).$ Take the logs of each variable in

that equation and repeat the regression in log form $($not GS$5).$ You must create

the log variables before running this regression, call Model$2.$

mydata$logPCEC$96<-$log$($mydata$PCEC$96)$

mydata$logDSPIC$96<-$log$($mydata$DSPIC$96)$

Another student wonders if interest rates $($GS$5)$ matters in consumption behavior.

Run another model that adds interest rates $($GS$5)$ to Model$2,$ call Model$3.$

Using stargazer $()$ to generate a nice Table $($call it Table $2)$ including all three regression

results for easy comparison.

Bring Table $1-2$ to your final exam.