Linear Regression

​Linear Regression

Multiple Choice

As x increases, y increases

• A) correlation coefficient

• B) causation

• C) positive correlation

• D) negative correlation

Multiple Choice

As x increases, y decreases.

• A) no correlation

• B) negative correlation

• C) correlation coefficient

• D) positive correlation

Multiple Choice

Average fat intake per citizen of a country and average cancer rate of a country.  $$r=.73$$  

• strong positive

• strong negative

• weak positive

• weak negative

I CAN......

• create scatterplot on graphing calculator (DESMOS)

• Determine line of best fit using a graphing calculator (linear regression.

• Make a prediction using linear regression equation.

Line of Best Fit

A line of best fit (or trend line) is a straight line that best represents the data on a scatter plot.

• Always represents the general trend of the of the data.

​aka Linear Regression Equation

Lines of Best Fit

The best line of fit goes through the center of the data, following the trend of the scatterplot

​Find the linear regression equation for the data set:

1. Click the plus sign on DESMOS Graphing Calculator

2. Click "table"

3. Enter the values​

4. On the next line​ under the table, type y1~mx1+b

5. Desmos will give you m and b. Plug them into y=mx1+b to get your equation! 

Equation is y=3x-1

Multiple Choice

A restaurant sells pizza for the prices in the data table. Calculate the linear regression equation of the data.

• y = 1.5x + 12

• y = 12x + 1.5

• y = 0.67x - 8

• y = -8x + 0.67

y = 1.5x + 12

Multiple Choice

What is the line of best fit?

• f(x)= 5x+1.82

• cannot be determined

• f(x)= 1.82x + 5.02

• f(x)= 1.1x + 4.2

Equation: y=1.82x+5.02

Multiple Choice

The chart below tracts starting salaries for health care workers since the year 2000. Using linear regression, find the equation of best fit. Round decimals to 3 places.

• y = 839.721x + 27541.812

• y = 27541.812x - 839.721

• y = 27541.812x + 839.721

• y = 839.721x - 27541.812

Multiple Choice

The linear regression equation is y = 61.93x - 1.79.  Use the equation to predict how far this person will travel after 10 hours of driving.

• 10 miles

• 617.5 miles

• 0.19 miles

• 500 miles

​Make predictions using the Linear regression equation

​1.) Find linear regression equation.

2. ) Substitute value in for x.

3.) Find predication for y.

4.) Answer the question

y=61.93x - 1.79

y=61.93(10) - 1.79

= 619.3 - 1.79

= 617.5

​The person is predicted to travel 617.5 miles in 10 hours.

Multiple Choice

The linear regression equation for the data is  y = 1.5x + 12.  Use the equation to predict the cost of a pizza that has 8 toppings.

• $8

• $12

• $24

• $28

​Interpretation of Linear Regression Equation

Multiple Choice

The linear regression equation for the data is y = 1.5x + 12. Interpret the slope of the equation.

• The slope is (0, 1.5). It means that a pizza with 0 toppings will cost 1.5 dollars.

• The slope is 1.5. It means that it costs 1.5 dollars per topping.

• There are 1.5 toppings.

• There are 1.5 pizzas.

Which statement below is the best interpretation of the y-intercept for the best-fit line?

Multiple Choice

A person travels by car. They record their miles driven in a data table. Calculate the linear regression equation of this data.

• y = 61.93x - 1.79

• y = -1.79x + 61.93

• y = 0.016x + 0.03

• y = 0.03x + 0.016

Multiple Choice

Write the linear regression equation for the following data points. Round to the nearest hundredth.

• $$y=-0.83x+0.61$$

• $$y=-0.83x+0.63$$

• $$y=0.83x+-0.8$$

• y = -0.828767x + 0.609589

Multiple Choice

If Joe worked 30 hours, how much is he expected to earn?

• $600

• $200

• $1000

• $800

Multiple Choice

Make a prediction for a resting heart rate after 6 hours of exercise a week.

• 6

• 50

• 55

• 59

Multiple Choice

Exit Ticket: What is the correlation coefficient and linear regression of the data set: (1,7) (2,4) (3,-1) (8,-9) (6,-3) (-1,10).

• r = .98 & y = 7.9x - 2.1

• r = .97 & y = 7.9x - 2.1

• r = .95 & y = 7.9x - 2.1

• r = .98 & y = -2.1x + 7.9

• r = .97 & y = -2.1x + 7.9

Open Ended

How well did you understand today's lesson? One of your classmates is absent today.  Write down one item that they should know based upon today’s lesson.