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

To complete this exercise you need a software package that allows you to generate data from the uniform and normal distributions.

(i) Start by generating 500 observations xi - the explanatory variable - from the uniform distribution with range [0,10]. (Most statistical packages have a command for the Uniform[0,1] distribution; just multiply those observations by 10.) What are the sample 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 commonly available, simply multiply the outcomes by six.) Is the sample average of the ui exactly zero? Why or why not? What is the sample standard deviation of the ui?

(iii) Now, generate the yi as

??=1+2??+??≡?0+?1??+??

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

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

??=0.5×??

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

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Expert Solution

genius_generous answered 1 year ago

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