Lab -06

[sunaynagoel]

When I regress the variable using linear model

==========================================================
                                   Dependent variable:    
                               ---------------------------
                                       Happiness-y        
----------------------------------------------------------
Income-X                                0.0002***         
                                        (0.00000)         
                                                          
Constant                                50.871***         
                                         (0.390)          
                                                          
----------------------------------------------------------
Observations                              2,000           
Adjusted R2                               0.690           
==========================================================
Standard errors in parentheses *p<0.1; **p<0.05; ***p<0.01

But when I regress the model using Quadratic model, I Get

==========================================================
                                   Dependent variable:    
                               ---------------------------
                                       Happiness-y        
----------------------------------------------------------
Income-X                                0.001***          
                                        (0.0001)          
                                                          
x_squared                                -0.000*          
                                         (0.000)          
                                                          
Constant                                30.714***         
                                         (0.657)          
                                                          
----------------------------------------------------------
Observations                               574            
Adjusted R2                               0.808           
==========================================================
Standard errors in parentheses *p<0.1; **p<0.05; ***p<0.01

I noticed b0 and b1 changed, with is understandable but observation sized decreased from 2000 to 574. Am I missing something ?

[sunaynagoel]

Please excuse bold format, I had no control on it.

just add fences  ``` around your code

[sunaynagoel]

Part 2. #1,2

The graph looks different on lab instruction and R studio. The outliers points A and B are at very different locations. Which one should we go by , lab instructions or R studio ?

[lecy]

@sunaynagoel Try re-loading the IncomeHappiness.csv data please. The file got corrupted when uploading to GitHub - it is fixed now.

URL <- "https://raw.githubusercontent.com/DS4PS/cpp-523-fall-2019/master/labs/data/IncomeHappiness.csv"
dat <- read.csv( URL )

The graph looks different on lab instruction and R studio. The outliers points A and B are at very different locations. Which one should we go by , lab instructions or R studio?

Here's what I get in R running the graph code. It's the same for me on both. Not sure what you are seeing?

Can you copy and paste the image into your question?

library( dplyr )

URL <- "https://github.com/DS4PS/cpp-523-fall-2019/blob/master/labs/data/np-comp-data.rds?raw=true"
dat <- readRDS(gzcon(url( URL )))
set.seed( 1234 )
d2 <- sample_n( dat, 2000 )

plot( log(d2$REVENUE), log(d2$SALARY), bty="n", pch=19, col="darkorange",
      xlab="Nonprofit Revenue (logged)", ylab="Executive Director Salary (logged)",
      xlim=c(5,25), ylim=c(5,16))
abline( h=seq( 1, 20, 0.5 ), col=gray(0.5,0.2), lwd=1 )
abline( v=seq( 1, 25, 0.5 ), col=gray(0.5,0.2), lwd=1 )
abline( lm( log(d2$SALARY) ~ log(d2$REVENUE) ), col=gray(0.5,0.5), lwd=3 )

[sunaynagoel]

@sunaynagoel Try re-loading the IncomeHappiness.csv data please. The file got corrupted when uploading to GitHub - it is fixed now.

It worked. so the number of observation show 2000 in both linear and quadratic regression. But the coefficient for B2 is -0.000, that takes away marginal effect of quadratic regression. Is that right ?

[sunaynagoel]

Can you copy and paste the image into your question?

Thats what mine looks like. but in in the instruction A is at top left extreme of X and B is sort of in the middle below the slope line. I haven't changed anything.

[lecy]

It's a conceptual question, you don't need to do any math. So just use the image in the lab.

But I suspect you didn't include the filter when you loaded the data?

URL <- "https://github.com/DS4PS/cpp-523-fall-2019/blob/master/labs/data/np-comp-data.rds?raw=true"
dat <- readRDS(gzcon(url( URL )))
set.seed( 1234 )
d2 <- sample_n( dat, 2000 )

It's a simplified dataset (sample of 2000 cases). It looks like you are plotting the full dataset there.

[lecy]

b2 is still significant, it's just a small number since x-squared is so big:

y <- dat$happiness
x <- dat$income 
x2 <- x*x
options( scipen=8 )
summary( lm( y ~ x + x2 ) )
                     Estimate        Std. Error t value Pr(>|t|)    
(Intercept) 35.34826872249551  0.36139931707627   97.81   <2e-16 ***
x            0.00073610233669  0.00000887024309   82.99   <2e-16 ***
x2          -0.00000000251607  0.00000000004385  -57.38   <2e-16 ***

You can simplify the print-out by changing the scale of X. A linear transformation (dividing by a constant) does not impact the model in any meaningful way other than changing the scale of measures:

y <- dat$happiness
x <- dat$income / 10000
x2 <- x*x
summary( lm( y ~ x + x2 ) )
Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) 35.348269   0.361399   97.81   <2e-16 ***
x            7.361023   0.088702   82.99   <2e-16 ***
x2          -0.251607   0.004385  -57.38   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

You just need to shift interpretation from b1 representing a $1 change in X to a $10,000 change in X.

[sunaynagoel]

Makes perfect sense. Thanks again

[sunaynagoel]

#1
when I produce regression table, it generates in R studio with this error . But when knit the document the table does not show up.

length of NULL cannot be changedlength of NULL cannot be changedlength of NULL cannot be changedlength of NULL cannot be changedlength of NULL cannot be changed

[jmacost5]

This is a dumb question, but is question 1 asking us to define each of the variables in the equation? Along with this would b0 be observation or would it be the constant?

[lecy]

@sunaynagoel I would need more information. What question, and what is your code?

[lecy]

@jmacost5 Yes, run the regression and report the table in Q1, then use the coefficients for Q2-Q4.

b0 is the constant (intercept).

[sunaynagoel]

@sunaynagoel I would need more information. What question, and what is your code?
It is or question #1
Here is my code. It is giving me the output I need in R studio. But when i Knit the table does not show up on my html document.

y <-  dat$happiness
x <- dat$income/10000
x_squared  <- x*x
m <- lm( y ~ x + x_squared, data=dat )
stargazer( m, type="text",
           dep.var.labels=c("Happiness-y"),
           covariate.labels=c("Income-X"),
           omit.stat = c("rsq","f","ser"),
           notes.label = "Standard errors in parentheses" )

[lecy]

Check the code chunk options. They should be:

{r, results="asis"}
stargazer( m, type="html", ... )

[sunaynagoel]

@lecy The link to submit the assignment is not working for me :)