Question

Can someone please explain how to do the steps for this? I already have part a completed but I need help with b-e. Thank you.

Problem 1:

(a) What is spurious regression? Explain.

(b) Assuming , randomly generate 1000 observations of variables X and Y using the following equations:

Report the graphs of X and Y.

(c) Run the regression: and report the estimated results.

(d) What did you expect about the magnitudes and R-square? How are the estimated values different from your expectations?

(e) In HW 2 problem 1, you estimated a regression of personal consumption expenditures (PCE) on personal disposable income (PDI). Both PCE and PDI were time series data. Explain why that regression was not spurious.

Answer 1

part b)

x=rnorm(n = 1000,mean = 0,sd = 1)
epsilon = rnorm(n=1000,mean = 0,sd = 2)
y = 0.5+ 2*x+ epsilon
summary(y)

Min. 1st Qu. Median Mean 3rd Qu. Max.
-7.5327 -1.3857 0.5624 0.5317 2.4416 10.5398

plot(x,y)c) model.linear = lm(y~x)
summary(model.linear)

Call:

lm(formula = y ~ x)

Residuals:

Min 1Q Median 3Q Max

-6.5487 -1.4064 -0.0183 1.3948 7.4133

Coefficients:

Estimate Std. Error t value Pr(>|t|)   

(Intercept) 0.38311 0.06352 6.031 2.29e-09 ***

x 2.00601 0.06510 30.813 < 2e-16 ***

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.003 on 998 degrees of freedom

Multiple R-squared: 0.4875, Adjusted R-squared: 0.487

F-statistic: 949.5 on 1 and 998 DF, p-value: < 2.2e-16

d) the magnitude of slope is showing positvely correlated with the response variate. and R square just 48.7 percent only contributing in the response of predictor variable.

e) i m guessing PCE as response variable and PDI as predictor variable are correlated to each other.based on the given information. i am giving you two reason for that

1) error and independent variable are orthogonal means independent to each other.

2) to check autocorrelation of error terms # so there is no autocorrelation in that model

3) similary autocorrelation of response variate.# as above autocorrelation

4)Spurious regression happens when there are similar local trends.# no trend in that model.