Goal: I can fit a linear function for a scatter plot that suggests a linear association. (S-ID.6)

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Presentation transcript:

Goal: I can fit a linear function for a scatter plot that suggests a linear association. (S-ID.6)

 Involves the relationship between two quantitative variables − an independent variable and a dependent variable.  One way to analyze such data is to graph the data. A scatterplot is a graph of two quantitative variables.

 Listen to the instructions for creating a scatterplot.  Based on the scatterplot, do you think there is a relationship between the amount of time spent studying and SAT math scores?

 Traffic Fatalities The following table represents the number of speeding‑related traffic fatalities on non‑interstate roads in California during Speed # of Fatalities

 TV Viewing Habits Some studies have shown that the number of hours spent watching television affects student grade point averages (GPAs). The following table represents the TV viewing habits of six students and their GPAs. Hours GPA

 Describes the relationship between two variables in a scatterplot. Data can have a positive correlation, a negative correlation, or no correlation.

 Identify the type of correlation.

Regression Model –  Another name for a model of best fit is a regression model.  Regression finds a model for bivariate data.  The regression model is the equation of a line or curve that "best fits" the given data.

 Notice that the linear regression is typically written in slope-intercept form, y = mx + b. The slope and y-intercept of the linear regression provides key information about the data set.  Recall that slope, or the rate of change, is the ratio of the change in the dependent variable y to the change in the independent variable x.  The y‑intercept is the point where a line crosses the y‑axis. Since the x‑coordinate for a y‑intercept is zero, the y‑intercept represents the starting value for the data set.

Size (in oz.) Price $ Size of coffee (in Oz.) Price (in dollars)

Steps to Determine the Equation of a Line of Best Fit (Linear Regression):  1. Create a scatterplot. (STAT – Edit; Set the window; Turn on the STAT PLOT; Check to make sure there are no equation in Y= screen  2. STAT CALC #4: LinReg(ax+b).  3. Arrow down to Store RegEQ: Y 1  4. To get Y 1 : Press then Y-VARS#1: Function ENTER, #1: Y 1 ENTER  5. Arrow to highlight Calculate ENTER  6. The calculator will give you values for a and b. Round these numbers to an appropriate place value and write down the values for a and b.  7. Using the values for a and b, enter the equation into Y=.  8. GRAPH.

Size (in oz.) Price $ Price (in dollars) Size of coffee (in Oz.)

 So far we've seen that a scatterplot can display a correlation between two variables.  Once the type of trend has been identified, we can use a model that best fits the scatterplot to make predictions.  Predictions is a statement about the future. It's an guess, that is based on facts or evidence (data).

Size (in oz.) Price $ Using the equation of the line of best fit we can make predictions… ? ? $5.82 $8.40