Linear RegressionLinear Regression

Linear RegressionsLinear Regressions

• So far, we have been graphing So far, we have been graphing ___________ functions. ___________ functions.

• In the real world, does all data fall on In the real world, does all data fall on a straight line?a straight line?

Line of best fitLine of best fit

A A line of best fitline of best fit is a straight line that is a straight line that best represents the data on a scatter best represents the data on a scatter plot.  plot. 

This line may pass through some of This line may pass through some of the points, none of the points, or all the points, none of the points, or all of the points.of the points.

Linear RegressionsLinear Regressions

• If I took a poll of If I took a poll of people at the people at the grocery store to grocery store to find out the find out the number of dollars number of dollars a family spent vs a family spent vs the number of the number of people in their people in their family….what family….what would this graph would this graph look like?look like?

Draw the graph, and a line of best Draw the graph, and a line of best fitfit

Positive correlationPositive correlation

• What does a positive correlation What does a positive correlation mean when discussing a “line of best mean when discussing a “line of best fit”fit”

• Discuss with your partner some Discuss with your partner some example of a relationship with a example of a relationship with a positive correlationpositive correlation

Positive CorrelationsPositive Correlations

• SAT scores and college achievementSAT scores and college achievement—among college students, those with —among college students, those with higher SAT scores also have higher higher SAT scores also have higher grades grades

Negative CorrelationNegative Correlation

• What does a positive correlation What does a positive correlation mean when discussing a “line of best mean when discussing a “line of best fit”fit”

• Discuss with your partner some Discuss with your partner some example of a relationship with a example of a relationship with a negative correlationnegative correlation

Negative CorrelationsNegative Correlations

• Education and years in jail—people who have more years of Education and years in jail—people who have more years of education tend to have fewer years in jail (or phrased as education tend to have fewer years in jail (or phrased as people with more years in jail tend to have fewer years of people with more years in jail tend to have fewer years of education) education)

• Crying and being held—among babies, those who are held Crying and being held—among babies, those who are held more tend to cry less (or phrased as babies who are held less more tend to cry less (or phrased as babies who are held less tend to cry more) tend to cry more)

• There is a negative correlation between TV viewing and class There is a negative correlation between TV viewing and class grades—students who spend more time watching TV tend to grades—students who spend more time watching TV tend to have lower grades (or phrased as students with higher have lower grades (or phrased as students with higher grades tend to spend less time watching TV).grades tend to spend less time watching TV).

Positive or NegativePositive or Negative

• The amount of time you spend gossiping about people and The amount of time you spend gossiping about people and the number of friends you have. the number of friends you have.

• Amount of hours you practice vs the number of games you Amount of hours you practice vs the number of games you win.win.