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Generate a variable containing the error terms using generate. Name this variable pred error.Generate summary statistics for the variable.

INSTRUCTIONS TO CANDIDATES
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Access the dataset home_sales_hw1_spring_2020.txt from our class page in Web courses. Using the Stata software, write and execute a do-file that performs the following steps. Submit to me hard copies of the program and the output requested below. 

A. Read the data in text format (.txt) into Stata and save the data as a Stata dataset (.dta) using ‘insheet’. 

B. To get a feel for the data, take a quick look at the dataset using the data editor and generate summary statistics for all of the variables. Print these summary statistics and write a brief description of your findings. 

C. Change the name of the variable ‘sale_def’ to ‘home_price’ and the name of the variable ‘area’ to ‘area_heated’ using ‘rename’. 

D. Generate histograms for the home_price and area_heated variables using ‘histogram’. Print both of these. 

E. Generate a scatter plot relating home_price to area_heated with home_price measured along the vertical axis and area_heated measured along the horizontal axis using ‘scatter’. Print this. 

F. Measure the relationship between home_price and area_heated by estimating a simple linear regression model using ‘regress’. Print the estimation results and discuss/interpret your findings. Specifically, discuss/interpret the estimated intercept and slope coefficients and the coefficient of determination (R2). 

G Obtain predicted values of home_price from the estimated model using ‘predict’. That is, generate a variable containing the predicted values, and name this variable ‘pred_price’. Generate summary statistics for the variable and for the dependent variable, home_price using ‘summarize’. Print the summary statistics. Is the mean predicted value equal to the sample mean of the dependent variable (consistent with the problem 8 from homework1)? 

H. Generate a variable containing the error terms using ‘generate’. Name this variable ‘pred_error’. Generate summary statistics for the variable. Print the summary statistics. Is the mean error equal to zero (consistent with problem 3 from homework 1)? 

I.   Use the regression output to perform hypothesis tests about the coefficients of the regression model. Specifically, use t-tests to test the null hypothesis that the coefficients are equal to zero against the alternative hypothesis that the coefficients are not equal to zero. Do this using pen/pencil and paper. In the process, be certain to: 

i) Write out the null hypothesis and alternative hypothesis.

ii) Calculate the t-statistics and specify the critical value associated with the 1% level of significance.

iii) Compare the t-statistics to the critical value.

iv) State whether you reject or fail to reject the null hypotheses.

v) State your conclusions regarding your findings about the relation between home_price and area_heated. 

J.  Lastly, confirm the result shown in problem 4 from homework 1. Specifically, estimate a regression model with the dependent and independent variables expressed in deviation form and the intercept term suppressed (i.e., fixed at a value of zero) and show that the estimated slope coefficient is equal to that value of the slope coefficient obtained in part F above. 

To do this, you’ll need to generate a ‘transformed’ dependent variable and ‘transformed’ independent variable by subtracting the respective sample means from the original variables (using the ‘summarize’ and ‘generate’ commands) and then estimate the model using Stata’s ‘regress’ command including the ‘noconstant’ option

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