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To complete this exercise you need a software package that allows you to generate data from...

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Physics

To complete this exercise you need a software package thatallows you to generate data from the uniform and normaldistributions.

(i) Start by generating 500 observations xi - the explanatoryvariable - from the uniform distribution with range [0,10]. (Moststatistical packages have a command for the Uniform[0,1]distribution; just multiply those observations by 10.) What are thesample mean and sample standard deviation of the xi?

(ii) Randomly generate 500 errors, ui, from the Normal[0,36]distribution. (If you generate a Normal[0,1], as is commonlyavailable, simply multiply the outcomes by six.) Is the sampleaverage of the ui exactly zero? Why or why not? What is the samplestandard deviation of the ui?

(iii) Now, generate the yi as

??=1+2??+??≡?0+?1??+??

that is, the population intercept is one and the populationslope is two. Use the data to run the regression of yi on xi. Whatare your estimates of the intercept and slope? Are they equal tothe population values in the above equation? Explain.

(iv) Repeat parts (i), (ii), and (iii) with a new sampleof data, starting with generating the xi

??=0.5×??

Now what do you obtain for b0 and b1? Why are thesedifferent from what you obtained in part (iii)? Explain why indetail.

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