Common Core Algebra Unit 7 Extension: Linear Regression 12/20/16Lesson 2: Regression LinesObjective: SWBAT obtain a line of best fit and apply it to predict other values within the domain.Do Now:A survey was taken of 10 low and high temperatures, in Fahrenheit, in the month of April to try to establish a relationship between a day’s low temperature and high temperatures.

(a) Construct a scatter plot of this bivariate data set on the grid below.

(b) Would you characterize the relationship between the low and high temperature as a positive correlation or a negative correlation? Explain.__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________Group Task:(c) With a straight edge draw a line of best fit through this data set in the do now.(d) Calculate the slope of this line by picking off two points (not necessarily data points).

(e) Write the equation of this line using the slope you found in part d and one point.

(f) Use your line of best fit to estimate the high temperature for a day in April given that the low temperaturewas 42 degrees. Illustrate your answer on your graph.

Notes: Line of Best FitA ______________________________ (or "trend" line) is a straight line that best represents the data on a scatter plot. This line may pass through some of the points, none of the points, or all of the points.

Steps for Determining an Approximate Line of Best Fit:Step 1: Sketch a line through your points that put approximately half of the points above the line and half the points below the line.Step 2: Choose 2 points that your line crossed through.Step 3: Calculate the slope between these 2 points.Step 4: Pick-A-Point! (choose one of the 2)Step 5: Write the equation of your approximated line given the slope and a point.

Model Example:A bird watching group tracks the number of birds they see and the temperature for six different occasions. The data are collected on the table below.(a) Create a scatterplot from the given data.

(b) Sketch the line of best fit.(c) Determine the approximate equation for the line you created.

Approximate Line: ___________________

Exact Line (On Calculator): __________________________

(d) Use your linear model to predict how many birds they would see if the temperature were 55°.Approximate Line Prediction: ____________________________

Exact Line Prediction: _____________________________

Calculating the Line of Best Fit by hand only gives us an approximation… to find the EXACT Line, Use the calculator.

Press Stat > Edit > Enter your x-values in L1. > Enter your y-values in L2. > Stat > Calc > 4: LinReg ax + b

Check for Understanding:A car dealership keeps track of how many cars they sell at different prices. The data are collected on the table below.(a) Create a scatterplot from the given data.

(b) Calculate the line of best fit (regression equation) that relates cars sold (C) to price (P). Round values to the nearest hundredth.

(c) Use your model to predict how many cars they would sell at a cost of $31,000.

Group Task:In reality, the data shows that if the cost of a car is $25,000, 150 cars will be sold. Let’s see what the model says. Plug 25 in for x and predict how many cars should be sold according to the model.

Notes: ResidualsA residual is the difference between the actual value and the predicted value for a given x in the domain.

So for a $25,000 car, let’s calculate the residual:

Residual = Actual – Predicted

A line of best fit is “best” because it minimizes all of the residuals as best as possible. This is why it is GREAT to have a calculator or computer calculate this for you!Check for Understanding:Calculate the residual for a car worth $40,000.

Lesson Summary: In order to predict data from information that follows a linear pattern, we can use the equation from the __________________________________________.

The residual is the ______________ - _______________ values to show the difference between the x value (domain).

Problem Set:1. (a) Make a scatter plot of the data.

(b) Describe the correlation.

(c) Calculate the line of best fit.

(d) Use the model to predict a y-value given an x-value of 5.

X Y2 164 126 28 610 2

(e) Calculate the residual for an x-value of 8. 2. (a) Create a scatter plot of dollars spent versus hours in a mall.

(b) Describe the correlation.

(c) Calculate the line of best fit. (d) Use the model to predict the amount of money spent after 4 hours in the mall.

(e) Calculate the residual for 5 hours in the mall.

3. The scatter plot below shows the profit, by month, for a new company for the first year of operation. Kate drew a line of best fit, as shown in the diagram.

Hours in Mall 10 8 9 3 1 2 5 6 7 8 2 3

Dollars spent 40 15 24 20 10 35 50 70 18 25 100 60

Using this line, what is the best estimate for profit in the 18th month?1) $35,0002) $37,7503) $42,5004) $45,0004. Based on the line of best fit drawn below, which value could be expected for the data in June 2015?

1) 2302) 3103) 4804) 540

5. The number of hours spent on math homework each week and the final exam grades for twelve students in Mr. Dylan's algebra class are plotted below.

Based on a line of best fit, which exam grade is the best prediction for a student who spends about 4 hours on math homework each week?1) 622) 723) 824) 92

5. The graph below illustrates the number of acres used for farming in Smalltown, New York, over several years.

Using a line of best fit, approximately how many acres will be used for farming in the 5th year?1) 02) 2003) 3004) 400

6. A scatter plot was constructed on the graph below and a line of best fit was drawn.

What is the equation of this line of best fit?1)2)3)4)

7. Which equation most closely represents the line of best fit for the scatter plot below?

1)2)

3)

4)

8. Megan and Bryce opened a new store called the Donut Pit. Their goal is to reach a profit of $20,000 in their 18th month of business. The table and scatter plot below represent the profit, P, in thousands of dollars, that they made during the first 12 months.

Draw a reasonable line of best fit.

Using the line of best fit, predict whether Megan and Bryce will reach their goal in the 18th month of their business. Justify your answer.

Name ________________________________________ Exit SlipCommon Core Algebra Unit 7 Extension: Linear Regression 12/20/16Lesson 2: Regression LinesObjective: SWBAT obtain a line of best fit and apply it to predict other values within the domain.The table below shows the number of prom tickets sold over a ten-day period.

Plot these data points on the coordinate grid below. Use a consistent and appropriate scale. Draw a reasonable line of best fit and write its equation.

Name ________________________________________ Exit SlipCommon Core Algebra Unit 7 Extension: Linear Regression 12/20/16Lesson 2: Regression LinesObjective: SWBAT obtain a line of best fit and apply it to predict other values within the domain.The table below shows the number of prom tickets sold over a ten-day period.

Plot these data points on the coordinate grid below. Use a consistent and appropriate scale. Draw a reasonable line of best fit and write its equation.