Linear Regression Day 2

Correlation between distance running and weight of an individual

If the distance ran increases, what typically happens to the weight of the person?

Multiple Choice

The scatterplot shows what type of correlation?

• positive correlation

• negative correlation

Multiple Choice

Does the data show a good or bad fit to the line?

• good fit

• bad fit

Multiple Choice

If the data shows a negative correlation with a bad fit to the linear regression, which of the following is true about the coefficient correlation?

• r is close to 1

• r is close to -1

• r is close to 0

Multiple Choice

If the data shows a negative correlation with a correlation coefficient close to 0, which of the following is the most likely to be the correlation coefficient?

• r= 0.85

• r= -0.85

• r= -0.15

• r=0.15

• A correlation is strong if the data points are close to the line. The correlation coefficient (r) is close to 1 or -1.

• A correlation is weak if the data points are far from the line. The correlation coefficient (r) is close to 0.
  

​Strong vs Weak correlations

Categorize

Options (4)

Match each scatterplot to the correct type of correlation

Strong positive correlation

Strong negative correlation

Weak positive correlation

Weak negative correlation

Linear Regression in the Calculator

1. Turn on STAT DIAGNOSTICS (press the mode button)

2. Make two lists in L1 (x) and L2 (y) (stat, Edit)

3. Go to 4:LinReg(ax+b) (stat, CALC, option 4)

4. Calculate. Make sure you see y=ax+b, a=, b=, r²=, and r

   r is the correlation coefficient!

​State the linear regression equation for this data set, rounding all values to the nearest hundredth.

State the correlation coefficient, rounded to the nearest hundredth.

​ State what this correlation coefficient indicates about the linear fit of the data.

Math Response

Write the linear regression equation for this data set, rounding all values to the nearest hundredth.

Write it as $$y=ax+b$$ , where a and b are replaced with numbers.

Type answer here

Correct Answer: y=-37.57x+215.67

Deg^°

Rad

Math Response

State the correlation coefficient to the nearest hundredth.

Type answer here

Correct Answer: -0.98

Deg^°

Rad

Open Ended

State what this correlation coefficient indicates about the linear fit of the data. What does the value of r say about how well the data approximates a line?