Linear Regressions and Scatterplots

Scatterplots & Linear Regression

Types of Data

• Categorical (Qualitative) Data: eye color, favorite subject, zip code, favorite animal

• Numerical (Quantitative) Data: Height, weight, number of students in a class

• To determine if data is categorical or numerical, ask if a meaningful average exists.

Scatterplots

• Only for numerical/quantitative data

Scatterplots

* A graph of a set of data points (x,y)

* A way to determine if 2 variable are related to each other

*Example:

Open Ended

Give an example of when scatterplots would be useful outside of the classroom.

Independent variable (x) vs. Dependent variable (y)

• Think of it in terms of cause and effect: the independent variable (x) causes the dependent variable (y)

• y "depends" on x

• The dependent variable is always graphed on the vertical y-axis and the independent variable is always graphed on the horizontal x-axis

Multiple Choice

Molly investigated if the age of students caused them to be better drivers. What is the INDEPENDENT VARIABLE?

• Type of car

• Skill of driving

• Age

Multiple Choice

The higher the temperature in the skillet, the faster the egg will cook. Select the INDEPENDENT VARIABLE.

• Time

• Temperature

Multiple Choice

Carey and Justin are raising money to purchase books for the library. The more money they raise, the more books they will be able to purchase for the library.

Which of the variables is the DEPENDENT VARIABLE?

• amount of money raised

• number of books

Multiple Choice

What type of association does this graph have?

• positive
• negative
• none
• all of the above

Multiple Choice

What type of association does this graph have?

• positive 
• negative
• none
• all of the above

Poll

Does this scatterplot have a positive or negative correlation?

• Positive

• Negative

Multiple Choice

What type of association does this scatter plot represent?

• positive linear association
• negative linear association
• no association
• nonlinear association

Outliers

• Extreme values that are either very large or very small with respect to the rest of the data points

Correlation coefficient

Multiple Choice

Estimate the correlation coefficient

• r = 1

• r = -1

• r ≈ -0.8

• r ≈ 0.8

• r ≈ -0.5

Multiple Choice

Estimate the correlation coefficient.

• r is close to 1

• r is close to -1

• r is close to 0

• r is close to -0.5

• r is close to 0.5

Multiple Choice

Estimate the correlation coefficient.

• r is close to zero

• r is close to -1

• r is close to 1

• r is close to -1.5

• r is close to 1.5

Why linear regression?

Use linear regression to predict the outcome of a progression using a given set of data.

Example #1

• Click on STAT

• Click on Edit

• Enter the data into L1 and L2

• Click STAT, then right to CALC

• Scroll down to LinReg(ax+b)

• Click Enter, then Enter again

Example #2

• Click on STAT

• Click on Edit

• Enter the data into L1 and L2

• Click STAT, then right to CALC

• Scroll down to LinReg(ax+b)

• Click Enter, then Enter again

Multiple Choice

Write the equation for the table given

• y = 1/3x
• y = 3x
• y = 1/2x

Multiple Choice

Write the equation for the linear regression shown.

• $$y=ax+b$$

• $$y=0.6x+0.1$$

• $$y=0.72x+r$$

• $$y=0.1x+0.6$$

Multiple Choice

Write the equation for the linear regression shown.

• $$y=-5.11x+3.23$$

• $$r=0.8$$

• $$y=3.23x\ -\ 5.11$$ $$\$$

• $$y=0.64x+0.8$$

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

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

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

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 Select

What is the correlation coefficient of the following data set?

(1,7) (2,4) (3,-1) (8,-9) (6,-3) (-1,10)

• r = .98

• r = .95

• r = .97

• y = -2.1x + 7.9

• y = 7.9x - 2.1

Multiple Choice

If x is temperature and y is coffee sales, use the following formula to determine the coffee sales on a 34° day.

y = -60x+6443

• $4403

• $4673

• $8483

• $6443