Ch. 13Inferential Statistics 13.1 Line of Best Fit

Linear Regression Test Student Selected PSAT IB A Statistician wants to know if there is a correlation between PSAT math scores and the Math Studies IB exam scores. She collected the following data from 10 randomly Selected students a)Is there a correlation between PSAT and IB math test scores? b)What kind of correlation is it? c)Draw the scatter plot showing the data collected d)Draw the line of best fit. e)If a PSAT score is 57, predict the corresponding IB score f)If an IB score was a 2, predict the corresponding PSAT score

Line of Best Fit notes Usually graphed in quadrant 1 One of the easiest ways to graph is find the mean point and y-intercept Predicting values that lie inside the data rangeis called interpolation Predicting values that lie outside the data range is called extrapolation.

The r-value is a correlation coeffient - r lies between -1 and 1 -When r = 1, there is a perfect positive correlation between variables -When r = -1, there is a perfect negative correlation between variables -When r is between -1 and -0.8 there is a strong negative correlation between variables -When r is between -0.8 and -0.6 there is a moderate negative correlation between variables -When r is between -0.6 and -0.4 there is a weak negative correlation between the variables -When r is between -0.4 and 0, there is no correlation between the variables.

r - value Is the covariance - Covariance will always be given - Concept is beyond this course Is the standard deviation of the x values Is the standard deviation of the y values

Example 2 If = , use the data given in example 1 and calculate the r-value.

Line of Best Fit formula

Example 3 Using the line of best fit formula and the following information, find the equation of the line of best fit in slope-intercept form – Mean point (14.4, 35.2) – = 9.23 – = 3.46

Example 4 A AP student collected data to determine if there is a correlation between the age of a high school student and the number of hours of homework he/she did per week. Age (x) Hours (y)

1)Draw a scatter plot 2)Determine the r-value a) Using your GDC b) Using the formula given that the covariance is ) Interpret the r-value as it relates to the relationship between the variables 4) Determine the equation of the regression line a) Using your GDC b) Using the formula 5) Construct a regression line of the r-value suggests a correlation between the variables 6) By drawing lines on your graph predict a) The number of hours, to the nearest hour, a 15-year-old student will study each week b) the age, to the nearest half-year, of a student who studies 2 hours per week. 7) Use the equation of the regression line and predict a) the number of hours, to the nearest hour, a 13.5-year-old student will study each week b) the age, to the nearest half-year, of a student who studies 16 hours per week.