这个作业是用回归分析计算教育支出占GDP和劳动力百分比之间的关系

MNGT 213: Assessment 3 Questions

It is believed that educational attainment is higher in countries with higher expenditure on

education as a percentage of GDP. Assuming that there is a linear relationship between

expenditure on education as a percentage of GDP and percentage of labour force (over 25

years old) with at least post-secondary education for 14 countries in the World Socioeconomic

Data, answer the following questions using the dataset labour force2015.xlsx.

(a) Calculate the sample correlation coefficient for the data. Comment on its value.

[5 marks]

(b) Explain your choice of independent and dependent variables.

[5 marks]

(c) Let y = Percentage of labour force with at least post-secondary education and x =

Expenditure on education as percentage of GDP. Use the Excel Data Analysis Add-in to

regress y on x. Interpret the regression coefficients. [10 marks]

(d) Plot the data and add the estimated regression line. [5 marks]

(e) Find the coefficient of determination (R2

) for the above estimated regression line and

give a full interpretation of the value. [5 marks]

(f) Perform a hypothesis test at the 5% significance level for the gradient of the regression

line and draw conclusions about whether there is evidence for a relationship between

Expenditure on education as percentage of GDP and Percentage of labour force with at

least post-secondary education. [10 marks]

(g) Produce appropriate plots of the regression residuals to assess the assumptions of the

regression model. Consider if there are any patterns in the residuals, which might

suggest ways to improve the model. For example, are the residuals normally distributed

and do they have constant variance? [10 marks]

(h) Predict the percentage of the labour force with at least post-secondary education for

Argentina based on the fact that the country’s expenditure on education in 2015 was

5.78% of GDP. Produce a 95% confidence interval for this prediction. [10 marks]

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