Data set: https://drive.google.com/file/d/1AWKgKqM9U6kVqskq8Wk6aMMVflAYM7-V/view

We want to analyse the relationship between the wages and IQ of the employees of a firm. We have a random sample of 935 employees. The variable wage contains the wages of the employees in thousands of rupees. The variable IQ contains their IQ scores. The variable educ contains their number of years of education. One model that explains the relationship 2 between wages and IQ is = 0+ 1+ , (1) where we define 1 to be the causal effect of IQ on wage. 1. What kind of factors might be contained in ? Are these likely to be correlated with IQ? 2. Will a simple regression of wage on IQ uncover the causal effect of IQ on wage? Explain. 3. What are the average values of wage and IQ in the sample? What are their minimum and maximum values? 4. How would you characterize the relationship between wage and IQ in terms of (a) direction, (b) linearity, and (c) strength? 5. What is the correlation coefficient between wage and IQ? Is this what you expected based on your characterization in part 4? 6. Estimate the model in (1) using OLS. (a) Interpret the estimated intercept 0 (b) Interpret the estimated coefficient 1. Does it have the sign that you would expect? 7. In terms of the model parameters, state the null hypothesis that IQ is not (linearly) associated with wage. State the alternative hypothesis that a higher IQ is associated with a higher wage. 8. Can you reject the null hypothesis in part 7 against the alternative hypothesis in part 7 at the 5% significance level? Suppose that instead of (1), we estimate the model =0+1+2+ (2) 9. What are the average, minimum, and maximum values of educ in the sample? 10. Estimate the model in (2) using OLS. (a) Interpret the estimated intercept 0.Does the intercept make sense? (b) Interpret the estimated coefficients 1 and 2 . 3 11. Regress educ on IQ and verify the omitted variable bias formula 1=1+ 21, where all notation is as in the lecture slides. 12. What is the predicted wage of the first individual in the sample according to the estimate of model in (2)? Is this individual overpaid or underpaid?