The Programme for International Student Assessment (PISA) is a worldwide study by the Organisation for Economic Co-operation and Development (OECD) in member and non-member nations intended to evaluate education systems by measuring 15-year-old school

pupils' scholastic performance in Mathematics, Science and Reading.

Refer to Math_and_gender dataset. The dataset contains the mean PISA Math scores for samples of 15-year-old male and female students from a number of randomly selected schools in each of various nations.

You are to perform a regression analysis using mean male score as the explanatory variable and mean female score as the response variable.

Perform the following:

(a)draw a scatterplot (excel) of female mean score vs male mean score, and include the regression line on the scatterplot.

(b)Interpret the slope in the context of this problem.

(c)Use the equation of the least-squares regression line to predict the female mean (Math) score for Singapore.

(d) Produce a residual plot (that is, plot residuals vs male means).

(e)What is/are the purpose(s) of a residual plot in regression analysis?For the residual plot drawn in part (d), explain what you learn in the context of this problem.

(f)Produce a histogram of the residuals. (show your work)-excel

(g)What is the purpose of drawing a histogram of the residuals in regression analysis? For the histogram of residuals drawn in part (f), explain what you learn.

(h)Identify two countries whereby the female students perform much worse than predicted based on the country's male mean score?

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