Slide Slide 1 Warm Up Page 536; #16 and #18 For each number, answer the question in the book but also: 1)Prove whether or not there is a linear correlation by using your calculator to find the p-value. 2) Is your answer the same as when you used table A-6? 3) Interpret r-squared for each question.

Slide Slide 2 Section 10-3 Regression

Slide Slide 3 Consider the following list of sixteen factors. Eight of the factors have a strong correlation (+ or -) with test scores; the other eight don’t seem to matter. Its taken from the 2005 best selling book Freakanomics. Try to guess which are which: 1) The child has highly educated parents. 2) The child’s family is intact. 3) The child’s parents have high socioeconomic status. 4) The child’s parents recently moved into a better neighborhood. 5) The child’s mother was 30 or older at the time of the first child’s birth. 6) The child’s mother didn’t work between birth and kindergarten. 7) The child had low birth weight. 8) The child attended Head Start. 9) The child’s parents speak English in the home. 10) The child’s parents regularly take him/her to museums. 11) The child is adopted. 12) The child is regularly spanked. 13) The child’s parents are involved in the PTA. 14) The child frequently watches television. 15) The child has many books in his home. 16) The child’s parents read to him nearly every day. Which ones correlate with test scores?

Slide Slide 4 Key Concept The key concept of this section is to describe the relationship between two variables by finding the graph and the equation of the straight line that best represents the relationship. The straight line is called a regression line and its equation is called the regression equation.

Slide Slide 5 Part I: Regression The typical equation of a straight line y = mx + b is expressed in the form y = b 0 + b 1 x, where b 0 is the y -intercept and b 1 is the slope. ^ The regression equation expresses a relationship between x (called the independent variable, predictor variable or explanatory variable), and y (called the dependent variable or response variable). ^

Slide Slide 6 Requirements 1. The sample of paired ( x, y ) data is a random sample of quantitative data. 2. Visual examination of the scatterplot shows that the points approximate a straight-line pattern. 3. Any outliers must be removed if they are known to be errors. Consider the effects of any outliers that are not known errors.

Slide Slide 7 Definitions  Regression Equation Given a collection of paired data, the regression equation  Regression Line The graph of the regression equation is called the regression line (or line of best fit, or least squares line). y = b 0 + b 1 x ^ algebraically describes the relationship between the two variables.

Slide Slide 8 Notation for Regression Equation y -intercept of regression equation  0 b 0 Slope of regression equation  1 b 1 Equation of the regression line y =  0 +  1 x y = b 0 + b 1 x Population Parameter Sample Statistic ^

Slide Slide 9 Formulas for b 0 and b 1 Formula 10-2 n(  xy) – (  x) (  y) b 1 = (slope) n(  x 2 ) – (  x) 2 b 0 = y – b 1 x ( y -intercept) Formula 10-3 calculators or computers can compute these values

Slide Slide 10 The regression line fits the sample points best. Special Property

Slide Slide 11 Rounding the y -intercept b 0 and the Slope b 1  Round to three significant digits.  If you use the formulas 10-2 and 10-3, try not to round intermediate values.

Slide Slide Data x y Calculating the Regression Equation In Section 10-2, we used these values to find that the linear correlation coefficient of r = – Use this sample to find the regression equation.

Slide Slide 13 Calculating the Regression Equation - cont n = 4  x = 12  y = 23  x 2 = 44  y 2 = 141  xy = 61 n(  xy) – (  x) (  y) n(  x 2 ) –(  x) 2 b 1 = 4(61) – (12) (23) 4(44) – (12) 2 b 1 = b 1 = = – Data x y

Slide Slide 14 Calculating the Regression Equation - cont b 0 = y – b 1 x 5.75 – (–1)(3) = Data x y n = 4  x = 12  y = 23  x 2 = 44  y 2 = 141  xy = 61

Slide Slide 15 Calculating the Regression Equation - cont The estimated equation of the regression line is: y = 8.75 – 1x ^ Data x y n = 4  x = 12  y = 23  x 2 = 44  y 2 = 141  xy = 61

Slide Slide 16 A teacher has designed a test he thinks will predict whether a student will do well in an introductory French class. He gave the test to 10 randomly selected students, then recorded each student’s final French grade  a)Is there a linear correlation between the test scores and the final French grade? b)Find the LSRL that can be used to predict the final French grade based on the test score using the formulas. c)Predict a value for the Final Grade when the Test Score was 40. StudentTest Score Final Grade