We got to know the Phillips Curve in the last assignment. In this assignment, we will use a linear
regression model to understand the relationship between the Consumer Price Indices (CPI) and the
Initial Jobless Claims (IJC). When the price is low, customers can get better bargains and subsequently
purchase more goods and services. This will put pressure on businesses to produce more and faster.
This, in turn, may drive up the demand for workers. To meet the demand, employers will compensate
workers more to attract the scarce pool of the right talents. These workers-turned-consumers will then
have more discretionary income to purchase goods and services. If that happens, prices will go up
because either supply is limited, or merchants see opportunities to collect more profits.
During prolonged periods of rising prices, the cost of running a business is more expensive (e.g., workers
demand higher compensation or higher costs of materials). To avoid losses, merchants will either raise
the prices of goods and services or reduce the costs of producing goods and services. A popular costcutting method is to reduce headcounts. Thus, this will lead to higher unemployment. Unfortunately,
the vicious cycle continues. When higher unemployment persists, customers tend to spend only on
necessities. Thus, fewer goods and services are purchased. This will put downward pressure on prices.
In this assignment, you will use the data from the CPI_IJC_2012_2022.xlsx file to measure the impact on
unemployment by rising prices. Like the previous assignment, you will create the Period variable here.
When Year is less than 2020, the Period is 1 (pre-pandemic). When Year is 2020, then the Period is 2
(pandemic). Otherwise, the Period is 3 (post-pandemic).
You will denote the monthly Consumer Price Indices by ?? and the weekly Initial Jobless Claims by ??. You
will formulate the relationship by this formula ?? = ?? ??+???? ???? , ?? = 1,2,3. The parameters are ??, ??, ??1 , ??2 ,
and ??3 . The latter three parameters depend on the Period.
Please round your answers, whenever applicable, to the seventh decimal place.
Question 1 (10 points)
You will generate a scatterplot of log ?? ?? versus log ?? ??, and color-code the points according to the values
of Period. Please label the axes properly, add gridlines, and display a legend to receive full credits.
Question 2 (20 points)
You will train a linear regression model of log ?? ?? on log ?? ??. Besides log ?? ??, the model also includes the
Intercept and the three dummy indicators for the Period. You will use the first period as the reference
category. What are the regression coefficients and their standard errors?
Question 3 (10 points)
What is the Coefficient of Determination of the linear regression model?
Page 1
Question 4 (20 points)
You will perform the appropriate statistical tests to check whether the linear regression model needs
Period or not. Your null hypothesis is ??0 : ??1 = ??2 = ??3 = 0. Your alternative hypothesis is ??1 : ???? ? 0 for
some ??. Please provide the test statistic, the degrees of freedom, and the significance value.
Question 5 (20 points)
You will perform the appropriate statistical tests to check whether log ?? ?? will affect log ?? ?? or not. Your
null hypothesis is ??0 : ?? = 0 and your alternative hypothesis is ??1 : ?? ? 0. Please provide the test
statistic, the degrees of freedom, and the significance value.
Question 6 (10 points)
The Consumer Price Index for All Urban Consumers in October 2022 is 298.062. What will the modelÊprediction for the Initial Jobless Claims (the original scale)? Please also provide the 95% confidence
interval for the mean Initial Jobless Claims under a normality assumption.
Question 7 (10 points)
You will calculate the Relative Error on the original scale of measurements. Let ???? and ????? denote the
observed and the predicted Initial Jobless Claims respectively. Also, let ??? denotes the mean of the
2
observed Initial Jobless Claims. The Relative Error is ???(???? ? ????? ) ????(???? ? ??? )2 . A small Relative Error
suggests a better-fitted model. What is the Relative Error of your regression model?
Page 2
Year Month
2012 JAN
2012 FEB
2012 MAR
2012 APR
2012 MAY
2012 JUN
2012 JUL
2012 AUG
2012 SEP
2012 OCT
2012 NOV
2012 DEC
2013 JAN
2013 FEB
2013 MAR
2013 APR
2013 MAY
2013 JUN
2013 JUL
2013 AUG
2013 SEP
2013 OCT
2013 NOV
2013 DEC
2014 JAN
2014 FEB
2014 MAR
2014 APR
2014 MAY
2014 JUN
2014 JUL
2014 AUG
2014 SEP
2014 OCT
2014 NOV
2014 DEC
2015 JAN
2015 FEB
2015 MAR
2015 APR
2015 MAY
2015 JUN
2015 JUL
2015 AUG
2015 SEP
2015 OCT
CPI
IJC
227.842
228.329
228.807
229.187
228.713
228.524
228.590
229.918
231.015
231.638
231.249
231.221
231.679
232.937
232.282
231.797
231.893
232.445
232.900
233.456
233.544
233.669
234.100
234.719
235.288
235.547
236.028
236.468
236.918
237.231
237.498
237.460
237.477
237.430
236.983
236.252
234.747
235.342
235.976
236.222
237.001
237.657
238.034
238.033
237.498
237.733
372000
365000
358000
372000
381000
372000
372000
377000
376000
364000
388000
362000
366000
342000
375000
331000
353000
340000
334000
325000
319000
347000
312000
332000
340000
341000
330000
345000
312000
308000
303000
303000
290000
291000
291000
285000
281000
317000
269000
269000
275000
275000
269000
279000
272000
275000
2015 NOV
2015 DEC
2016 JAN
2016 FEB
2016 MAR
2016 APR
2016 MAY
2016 JUN
2016 JUL
2016 AUG
2016 SEP
2016 OCT
2016 NOV
2016 DEC
2017 JAN
2017 FEB
2017 MAR
2017 APR
2017 MAY
2017 JUN
2017 JUL
2017 AUG
2017 SEP
2017 OCT
2017 NOV
2017 DEC
2018 JAN
2018 FEB
2018 MAR
2018 APR
2018 MAY
2018 JUN
2018 JUL
2018 AUG
2018 SEP
2018 OCT
2018 NOV
2018 DEC
2019 JAN
2019 FEB
2019 MAR
2019 APR
2019 MAY
2019 JUN
2019 JUL
2019 AUG
2019 SEP
238.017
237.761
237.652
237.336
238.080
238.992
239.557
240.222
240.101
240.545
241.176
241.741
242.026
242.637
243.618
244.006
243.892
244.193
244.004
244.163
244.243
245.183
246.435
246.626
247.284
247.805
248.743
249.439
249.581
250.146
250.779
251.118
251.323
251.749
252.239
252.862
252.657
252.551
252.470
253.135
254.273
255.163
255.325
255.361
255.900
256.179
256.596
265000
276000
282000
269000
271000
278000
263000
262000
266000
261000
247000
265000
255000
244000
241000
221000
236000
232000
253000
247000
245000
247000
260000
241000
243000
248000
223000
202000
205000
200000
224000
241000
222000
225000
221000
225000
244000
237000
227000
204000
173000
210000
222000
240000
220000
224000
224000
2019 OCT
2019 NOV
2019 DEC
2020 JAN
2020 FEB
2020 MAR
2020 APR
2020 MAY
2020 JUN
2020 JUL
2020 AUG
2020 SEP
2020 OCT
2020 NOV
2020 DEC
2021 JAN
2021 FEB
2021 MAR
2021 APR
2021 MAY
2021 JUN
2021 JUL
2021 AUG
2021 SEP
2021 OCT
2021 NOV
2021 DEC
2022 JAN
2022 FEB
2022 MAR
2022 APR
2022 MAY
2022 JUN
2022 JUL
2022 AUG
2022 SEP
257.305
257.788
258.263
258.682
259.007
258.165
256.094
255.944
257.217
258.543
259.580
260.190
260.352
260.721
261.564
262.200
263.346
265.028
266.727
268.599
270.955
272.184
273.092
274.214
276.590
278.524
280.126
281.933
284.182
287.708
288.663
291.474
295.328
295.271
295.620
296.761
230000
221000
235000
200000
190000
5946000
3446000
1639000
1446000
1260000
881000
795000
773000
737000
773000
803000
704000
658000
574000
427000
405000
414000
381000
376000
280000
240000
211000
214000
182000
171000
202000
202000
231000
248000
228000
190000

Purchase answer to see full
attachment