Common Core Algebra Unit 7 Extension: Linear Regression 12/22/16Lesson 4: Interpreting the Regression LineObjective: SWBAT interpret the meaning of the slope and y-intercept of a regression line in context of the problem.Do Now:

(a) Calculate the regression line.

(b) What is the slope of the line?

(c) What is the y-intercept of the line?

Turn and Talk:1) What do we know is true about the value of x at the y-intercept?

2) What would x = 0 mean in context of the above data?

3) Use the model to predict the Box Office Sales when Promo Costs are $0.

Notes:The y-intercept of the regression line predicts the “start value” of the relationship. It is the value of the dependent variable when x = 0.This value does not always need to make sense! It is just an arbitrary start point for the modeled relationship.Example: “If $0 is spent on promotions, it would yield box office sales worth $12.68 million dollars, which is possible.”

Promo Costs(millions)

First Year Box OfficeSales (in millions)

5.1 85.15.8 106.32.1 50.28.39 130.62.9 54.81.2 30.33.7 79.47.6 917.7 135.44.5 89.3

Group Task:1) What is the slope of the regression line?

2) How can you turn that slope into a fraction?

3) What is slope the ratio of?

4) If we put the slope ratio in context of the problem, what would our ratio be comparing?

Class Data Example:Ms. Hanna was asked to analyze the class heights and shoe sizes. Take 2 minutes to identify your height (in inches) (1 foot = 12 inches) and shoe size ( in men’s sizes) (girl’s > subtract 2 from your size).

Height ___________

Shoe Size __________

Height Shoe Size

Lesson Summary:

To interpret the meaning of the regression line, compare the _________ and the _______ of the slope.

Regression Line: ____________________

Correlation Coefficient: __________________

Check for Understanding:1) What is the slope of the regression line?

2) How can you turn that slope into a fraction?

3) What is slope the ratio of?

4) If we put the slope ratio in context of the problem, what would our ratio be comparing?

Problem Set:1) The heights (cm) and weights (kg) of 10 basketball players on a team are:

Height 186 189 190 192 193 193 198 201 203 205Weight 85 85 86 90 87 91 93 103 100 101

(a) Calculate the regression line.

(b) Predict the weight of a player with a height of 195 cm.

(c) Interpret the slope of the line in context of the problem.

(d) Interpret the y-intercept in context of the problem.

2) The following data tracks the number of hours worked in a factory and output units produced.

Hours 80 79 83 84 78 60 82 85 79 84Production 300 302 315 330 300 250 300 340 315 330

(a) Calculate the regression line.

(b) Predict the production of an employee who works 70 hours.

(c) Interpret the slope of the line in context of the problem.

(d) Interpret the y-intercept in context of the problem.

3. Fill in the table below and graph to see the relationship between the distance from Go and the cost of properties on a standard Monopoly board. Find the line of best fit when all data points have been graphed.

(a) Calculate the regression line.

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

(c) Interpret the y-intercept in context of the problem.

4. The accompanying table shows the enrollment of a preschool from 1980 through 2000.

(a) Write a linear regression equation to model the data in the table.

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

(c) Interpret the y-intercept in context of the problem.

5. In a mathematics class of ten students, the teacher wanted to determine how a homework grade influenced a student’s performance on the subsequent test. The homework grade and subsequent test grade for each student are given in the accompanying table.

a Give the equation of the linear regression line for this set of data.

(b) A new student comes to the class and earns a homework grade of 78. Based on the equation in part a, what grade would the teacher predict the student would receive on the subsequent test, to the nearest integer?

6. The accompanying table shows the percent of the adult population that married before age 25 in several different years.

(a) Using the year as the independent variable, find the linear regression equation. Round the regression coefficients to the nearest hundredth.

(b) Using the equation found above, estimate the percent of the adult population in the year 2009 that will marry before age 25, and round to the nearest tenth of a percent.

7. The data table below shows water temperatures at various depths in an ocean.

(a) Write the linear regression equation for this set of data, rounding all values to the nearest thousandth.

(b) Using this equation, predict the temperature (ºC), to the nearest integer, at a water depth of 255 meters.

8. The availability of leaded gasoline in New York State is decreasing, as shown in the accompanying table.

(a) Determine a linear relationship for x (years) versus y (gallons available), based on the data given. The data should be entered using the year and gallons available (in thousands), such as (1984, 150).

(b) If this relationship continues, determine the number of gallons of leaded gasoline available in New York State in the year 2005.

(c) If this relationship continues, during what year will leaded gasoline first become unavailable in New York State?

9. A factory is producing and stockpiling metal sheets to be shipped to an automobile manufacturing plant. The factory ships only when there is a minimum of 2,050 sheets in stock. The accompanying table shows the day, x, and the number of sheets in stock, .

(a) Write the linear regression equation for this set of data, rounding the coefficients to four decimal places.

(b) Use this equation to determine the day the sheets will be shipped.

10. The 1999 win-loss statistics for the American League East baseball teams on a particular date is shown in the accompanying chart.

Find the mean for the number of wins, , and the mean for the number of losses, , and determine if the point is a point on the line of best fit. Justify your answer.

11. Two different tests were designed to measure understanding of a topic. The two tests were given to ten students with the following results:

(a) Construct a scatter plot for these scores, and then write an equation for the line of best fit (round slope and intercept to the nearest hundredth).

(b) Find the correlation coefficient. (c) Predict the score, to the nearest integer, on test y for a student who scored 87 on test x.