Access the data in the burglary.xls file, which contains information about burglary arrests and employment levels for 90 counties in the United States.

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

Problem set 9

1. Access the data in the burglary.xls file, which contains information about burglary arrests and employment levels for 90 counties in the United States. Conduct a regression of Burglary Arrests vs. Employed(which contains the number of employed people in the civilian workforce

in that county.)

(a) What do these results suggest?

(b) Are these results surprising to you?

(c) Identify any counties that are outliers or highly leveraged of influential observations.

(d) What is the probability that a normal random variable will be over 5.6065 standard deviations from the mean (as the LA County residual is)?

2. Access the beerdata.xls dataset, which contains data on beer consumption and income levels per capita for 19 European counties. Con

duct a regression of beer consumption vs. income levels per capita.

(a) On average, as income increases by $1,000 per capita, how much does beer consumption increase?

(b) Does this relationship make sense?

(c) How would you answer to part a) if the outliers were removed from the data? (This is generally not a good idea, but we are using the

removal of outliers to see how strongly they impact some of our results.)

3. A Midwestern hotel chain has noticed much variation in its electricity costs and would like to be able to explain these changes for planning

and budgeting reasons. It lias collected samples from random hotels during random months during the past years. The variables include

the hotels’ electricity costs per room and the average temperature that month. These data are available in the electricitycosts.xls file. Use

R to conduct a regression of electricity costs per room vs. average temperature.

(a) Does the relationship seem significant?

(b) Plot residuals versus predicted values for this regression. Does this graph give you any thoughts on improving the model?

(c) Use the tools discussed in class to build an improved model.

4. Headhunter Inc.

Headhunter Inc, a firm specialized in worker recruiting for other firms, wants to perform an analysis of the  productivity  of their  typewrit- ing clerks.  They suspect that some of them are using computer skills to waste time in Facebook and Twitter instead of their typewriting jobs. For this they collect some data, which you can find in the file words.xls, on number of words typed per minute (Words), achieving score on a computer test (Computer) and experience measured in years of seniority in the job (Experience).

(a) They first run a regression to analyze the effect of computer skills on words typed, and they concluded that there is no evidence that computer skills are being used in social networks, because the effect is positive and statistically significant. Do you agree?

(b) Afterwards they included also Experience as an explanatory factor in the above regression. Is the regression in (a) biased? What is the size of the bias?

(c) Use an auxiliary regression of Experience as dependent variable and Computer as explanatory variable to explain the possible bias in (a) and (b), and to give a precise explanation on the effects ob- served (here you have to say what is the direct effect of Computer on Words, and what is the indirect effect).

5. The effects of different variables on education

A consultancy firm wants to analyze the effects of different variables on wages in the telecommunication sector in the UK. For this they buy a data set from the UK Office of National Statistics, consisting on survey with 935 family heads.

The data set education.xls consists in observations of wages (loga- rithm of monthly earnings), education (in years), IQ score and tenure (years with the actual employer). The label of the variables are lwages, educ, IQ and tenure, respectively.

Attachments:

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