Material Taken From: Mathematics for the international student Mathematical Studies SL Mal Coad, Glen Whiffen, John Owen, Robert Haese, Sandra Haese and Mark Bruce Haese and Haese Publications, 2004 AND Mathematical Studies Standard Level Peter Blythe, Jim Fensom, Jane Forrest and Paula Waldman de Tokman Oxford University Press, 2012

Scatter Plot Data Determine a linear equation that best-fits the data.

Line of Best Fit The problem with drawing a line of best fit by eye is that the line will vary from one person to the other.

The Regression Line The regression line for y on x is a more accurate version of the line of best fit, compared to best fit by eye. – It is also known as the least squares regression line. – It is the line drawn through a set of points such that the sum of the squares of the distance of each point from the line is minimum. If there is strong or moderate correlation, you can use the regression line for y on x to predict values of y for values of x within the range of the data.

Consider the set of points below. Square the distances and find their sum. we want that sum to be small. The Regression Line

The Regression Line Formula In exams you will only be expected to use your GDC to find the equation of the regression line. However, you may need to calculate it out by hand in your IA project. You should only calculate the equation of the regression line if there is a moderate or strong correlation coefficient. s x is the standard deviation for the x data values. s xy is the covariance.

Consider the data given: b) Estimate the value of y when x = 6. Comment on the reliability of your estimate. a) Given s xy ≈ , find the equation of the regression line. Practice

Remember! You should only calculate the equation of the regression line if there is a moderate or strong correlation coefficient. You cannot use the regression line to accurately predict values beyond the region of the given data.

The table shows the sales for Hancock’s Electronics established in late 1998: a) Draw a scatterplot to illustrate this data. b) Given that s xy ≈ 12.5 find the correlation coefficient, r. c) Find the equation of the regression line, using the formula. d) Predict the sales figures for the year 2006, giving your answer to the nearest $10,000. e) Comment on the reasonableness of this prediction. Practice

Regression Line with GDC TI 84 LinReg (ax + b) L1, L2 where L1 contains your independent data. and L2 contains your dependent data

The table shows the annual income and average weekly grocery bill for a selection of families: a)Construct a scatter plot to illustrate the data. b)Use your GDC to find r. c)Use your GDC to find the line of best fit. d)Estimate the weekly grocery bill for a family with an annual income of £ e)Comment on whether this estimate is likely to be reliable. Practice

Ten students train for a charity walk. The table shows the average number of hours per week that each member trains and the time taken to complete the walk. a)Use your GDC to find the correlation coefficient r. b)Use your GDC to find the equation of the regression line. c)Using your equation, estimate how many minutes it will take a student who trains 18 hours per week to complete the walk. Practice Training Time (hrs) Time for Walk (mins)

The table shows the number of mice for sale in a pet shop at the end of certain weeks. a)Use your GDC to find the correlation coefficient r. b)Use your GDC to find the equation of the regression line. c)Use your regression line to predict the number of mice for sale after 10 weeks. d)Can you accurately predict the number of mice after 20 weeks? Practice Time (x weeks) Number of Mice (y)