Linear Regression

Linear Regressions So far, we have been graphing ___________ functions. So far, we have been graphing ___________ functions. In the real world, does all data fall on a straight line? In the real world, does all data fall on a straight line?

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

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

Draw the graph, and a line of best fit

Positive correlation What does a positive correlation mean when discussing a “line of best fit” What does a positive correlation mean when discussing a “line of best fit” Discuss with your partner some example of a relationship with a positive correlation Discuss with your partner some example of a relationship with a positive correlation

Positive Correlations SAT scores and college achievement— among college students, those with higher SAT scores also have higher grades SAT scores and college achievement— among college students, those with higher SAT scores also have higher grades

Negative Correlation What does a positive correlation mean when discussing a “line of best fit” What does a positive correlation mean when discussing a “line of best fit” Discuss with your partner some example of a relationship with a negative correlation Discuss with your partner some example of a relationship with a negative correlation

Negative Correlations Education and years in jail—people who have more years of education tend to have fewer years in jail (or phrased as people with more years in jail tend to have fewer years of education) Education and years in jail—people who have more years of education tend to have fewer years in jail (or phrased as people with more years in jail tend to have fewer years of education) Crying and being held—among babies, those who are held more tend to cry less (or phrased as babies who are held less tend to cry more) Crying and being held—among babies, those who are held more tend to cry less (or phrased as babies who are held less tend to cry more) There is a negative correlation between TV viewing and class grades—students who spend more time watching TV tend to have lower grades (or phrased as students with higher grades tend to spend less time watching TV). There is a negative correlation between TV viewing and class grades—students who spend more time watching TV tend to have lower grades (or phrased as students with higher grades tend to spend less time watching TV).

Positive or Negative The amount of time you spend gossiping about people and the number of friends you have. The amount of time you spend gossiping about people and the number of friends you have. Amount of hours you practice vs the number of games you win. Amount of hours you practice vs the number of games you win.