1. Linear Models
We will determine and use linear models, and use correlation coefficients.

2. A cleaning company charges $100 for services and $5 per room.
Warm-Up:
A cleaning company charges $100 for services and $5 per room.
Write an equation in function notation and graph
What is the cost to clean 12 rooms?
How many rooms can be cleaned for $230?
This is a linear relationship.
Perfect

3. Warm-Up Answers Let r = the number of rooms and
C (r) = the total cost to clean r rooms.
Equation C(r) = r
C(12) = $160
230 = r
26 rooms

4. Avg. Wt. of US Girls Warm-Up: Age (yr) 0.5 1 2 3 4 6 8
Wt. (lb)
PLOT the points - why
Estimate a line visually (your judgment)
Pick two points ON the line to find model; note, the two points do NOT need to be part of the data set!
A. Calculate slope
B. Use y – y1 = m(x – x1) or y = mx + b

5. Regression Line on the Calculator
1) Enter data into STAT, 1:edit, L1 = I.V., L2 = D.V.
2) Plot on the calculator: STATPLOT, Type: scatterplot (1st one), Xlist = L1, YList = L2
ZOOM, 9:Zoomstat
3) Line of regression: STAT, →Calc, 4:LinReg (ax+b)
(to put into Y=: VARS, →Y-Vars, 1:Function, 1:Y1
4) Can also hand-type the equation into Y =
5) 9:ZoomStat to see line with points

6. Warm-Up
Use the calculator to find the line of regression for Average Wt. of US Girls
Use both equations to predict the weight of a girl who is 10.
What limitations do you see with this model?

7. Warm-Up Answers
y = 4.5x
60.01 pounds
Limitations?

8. 2 Main Reasons for Model s
Interpretation – what does the slope mean, what does the y-intercept mean?
Prediction – what will the weight be at 5 years old, when will the weight be 48 pounds?

9. Correlation:
a measure that describes the strength of the relationship between 2 variables
called correlation coefficient, r
value from -1 to 1, inclusive
closer |r| is to 1, stronger the correlation
sign indicates slope of the line
r = ±1 indicates perfect correlation

10. given r2, how can r be determined?
Correlation continuum: -1 1
weak -
weak +
strong -
strong +
none
weak – close to 0, little linear relation
strong – close to -1 or 1, good linear relation
given r2, how can r be determined?

11. How do I find r? Using your calculator…
Go to the catalog by pressing 2nd , 0
Scroll to the “D’s”
Highlight Diagnostic On, Enter
The r and r2 will now appear when you find your line of regression.

13. Which is more accurate? interpolation: extrapolation:
2 Types of Prediction:
interpolation:
predicts values between known data values
extrapolation:
predicts values beyond known data values
Which is more accurate?

14. Properties of a Linear Model: y =ax+ b
Concavity: None…there are no turning points.
Therefore, there are no inflection points.
End Behavior
When a > 0
Limx-∞f(x) = -∞
Limx∞f(x) = ∞
When a < 0
Limx-∞f(x) = ∞
Limx∞f(x) = -∞

15. Closure
The table below gives the age of a cat or dog and its corresponding age in human years.
Determine a line of regression, using the calculator.
What is the correlation coefficient and what does it tell you?
According to your equation, what happens to a dog or cats age as humans age one year?
car/dog age (years) .5 1 2 4 6 8 10 14 18 21
human age (years) 15 24 32 40 48 56 72 91
106

16. Closure Answers
y = 4.44x
r = .998; this indicates that the data is a very strong fit to the line; also, the rate of change (slope) is positive (as x increases, so does y.)
They age 4.44 years
Approximately 78.5 years; Interpolation; the input value is within the known data set.