Prob and Stats, Sep 23
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1 Prob and Stats, Sep 23 Calculator Scatter Plots and Equations of Lines of Fit Book Sections: 4.1 Essential Questions: How can the calculator help me to produce a scatter plot, and also the equation of a line of fit? How can I predict values? Standards: S.ID.6, 6a, 6b, 9
2 Opening Thought of the Day If you no have correlation between data sets, you cannot predict anything based on them! How do you know whether or not you have any (or sufficient) correlation? Ans Look at the scatter plot.
3 Seeing is Believing The simplest way to decide if a set of data has sufficient correlation to be modeled by the equation of a line (or any other function) is to plot it, look at, and make a decision about it. The question that begs asking is Would a line be a good model for this plot? Yes Your in business, find the equation No Might some other model fit?
4 For Our Purposes The graphing calculator is a sufficient tool to do the following: Produce a scatter plot of a reasonable sized set of data Compute a line of fit for that data, if applicable Compute some alternative function fit for the data, if deemed necessary Evaluate the quality of a function approximation to a set of data
5 The Evaluation Process Step-by-Step 1. Produce Enter data and graph relationship 2. View Look at the shape of the scatter plot 3. Assess Decide on a function model, get a feel for its quality. Is there no correlation? 4. If it applies, find the equation of a function of fit for the data. 5. Use A good model is used to make predictions (the purpose of this process)
6 Today s Goal To get comfortable with steps 1-5, in the context of the linear model To gain comfort, you must practice the procedure until you know it. We do that now.
7 Creating a Scatter Plot Produce and sketch a scatter plot of the data, follow along with everything today. You start from scratch on the first one, then restart from an appropriate point on the rest.
8 The Equation of a Line By Hand How do I find the equation of a line? You need two things: 1. Find m 2. Find b m y x 2 2 y x 1 1 b is the place where the line crosses the y axis Then plug m and b into y = mx + b
9 The Equation of a Line By Calculator How do I find the equation of a line by calculator? Have your x values in L 1 and y values in L 2, be comfortable with linear correlation Select [STAT] Calculate 4 (Linear regression), [ENTER] and you are presented with a and b. a is the slope (m) b is the y-intercept Then plug m and b into y = mx + b, you have an equation
10 Example 1 The average number of hours spent exercising by New Yorkers at each age is recorded. Produce a scatter plot and compute a line of fit for this data: Age, x Hours, y
11 Assessing Quality Trust your eyes or use the correlation coefficient, r, as a quality check. Graph your line on top of the scatter plot. To get r, turn DIAGNOSTICS ON on
12 When is it Non-Linear?
13 Everything Has Come Together You: Have created a scatter plot which has correlation Have derived an equation that fits the data Are satisfied with the quality of the model How do you make predictions based on your model? (Today we are only looking at linear models (y = mx + b))
14 Making Predictions You use the equation with additional possible data values (internal or external) to predict the value of the variable you want the prediction for. This is called variable substitution and expression evaluation, or equation sloving. Depending on which variable you use.
15 Mechanics vs Semantics The mechanics here are simple: What is y when x is some value, or what is x when y is some value. No problem will be worded like that. It will say what is one quantity vs another (names). That is semantics. You must learn to associate the name of something with its assigned variable.
16 Example 1 This data is linearly correlated with a line of fit equation: y = -.21x + 14 y here is hours, x is age!!!! a) About how many hours would a 40 year old exercise? b) About how many hours would a 65 year old exercise? c) About how old would a person who exercises 9 hours per week be?
17 Example 2 A line of fit equation for a small long-range aircraft fuel consumption for hours of flight (x) and gallons (y) is y = 3.95x a) About how many hours would a 25 gallons of fuel last? b) How much fuel would the plane use in 6 hours? c) How much fuel would the plane use in 10 hours?
18 Example 3 The heights and weights of the players on the Jackson High Flying Squirrels basketball team are as follows: Ht (in in.) Wt (in lbs) About how much would a 7ft tall player weigh (84 )? About how tall would a 130 lb player be?
19 Class work: CW 9/23/14, 1-7 HW Due 9/24/14, 1
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