(a) The following data shows annual earnings (measured in £) and years of work experience for a sample of 8 employees. Copy and paste the data from the table below in to Excel and use Excel to draw a scatter plot with the data. Ensure your graph is appropriately titled and labelled and then copy and paste the scatter plot in to your answer file. Comment on whether there is any evidence of a correlation between earnings and experience, and if so whether the correlation is positive or negative.
Earnings Experience
15000 16
8000 6
34000 12
25000 24
18000 25
23000 12
38000 48
19000 12
(b) Using the data in part a, calculate the correlation coefficient between earnings and experience, remembering to interpret your answer. Using a 5% significance level, test if the correlation coefficient obtained in part b is statistically significant.
(c) Using the data in part a, estimate a simple linear regression of the relationship between earnings and experience, i.e.
Earnings = a + b Experience +e
i. Interpret the intercept and slope coefficients and comment on whether the slope coefficient is statistically significant.
ii. Predict what an employee would expect to earn if they had 20 years of experience and if they had 16 years of experience.
iii. Interpret the goodness of fit, R2, for this regression, and use it to test if the model has any explanatory power. [HINT: use the Excel output]
(d) You are an assistant economist in the government, and you wish to analyse returns to education. Using data on a sample of 200 people you estimate the following regression using Ordinary Least Squares:
Earningsi = a + b1Experiencei + b2Educationi + b3Urbani + ei
where Earnings is annual earnings measured in £; Experience is the number of years a person has worked; Education is measured in number of years of schooling and Urban is a binary variable that is equal to 1 if the person lives in an urban area, and 0 otherwise.
You obtain the results shown in the Excel table below. Note that some information has been deliberately omitted.
R Square 0.432
Observations 200
Coefficients Standard Error t Stat
Intercept 14,325 1,862 7.693
Experience 215 86 BLANK
Education 650 218 BLANK
Urban 580 197 2.929
i. Interpret the coefficients of Experience, Education and Urban and comment on whether any of them are statistically significant.
ii. Outline briefly how you would attempt to improve this model (no more than 150 words)
Sample Solution
