Coordinate Algebra Day 1 Notes Date: _____ COMPLETED Scatter plots : show the relationship between two variables

Correlation : the degree to which two variables are associated

The graph below shows the relationship between height and age.

Height

Age

Although it isn’t linear, there is clearly a ____POSITIVE______correlation between age and height. This that as age increases, height increases.

The graph below shows the relationship between price of an object and the number purchased by customers.

# Purchased

Price

This illustrates a ______NEGATIVE___ correlation. This means as price of an object increases, the number purchased decreases. In other words, if the price of an object goes up, fewer people will buy that object.

The graph below shows the relationship between number of points scored on a test and height.

Points Scored

Height

There is no correlation between height and points scored because there is no definable pattern. Therefore, height and number of points scored on a test have no relationship. The , denoted by the letter r, is a number from -1 to 1 that measures the strength and direction of the correlation between two variables.

r r r (no correlation) (strong negative) (strong positive)

-1 0 1

When r is near 1: the points on a scatter lie close to a line with a positive slope there is a strong __positive___ correlation between the points

When r is near -1: the points on a scatter plot lie close to a line with a negative slope there is a strong __negative___ correlation between the points

When r is near 0: the points on a scatter plot do not lie close to any line plots are said to have __no____correlation

What would you say about the correlation of this plot? Negative Correlation

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

The equation of the best fit line is y = ax + b .

In this form, a is the slope of your best fit line and b is the y-intercept .

Ex1) Find an equation for the line of best for the plot to the right. The data and line are already drawn.

1. Pick two points on the line and find the slope between them.

Slope: (-4, 2) & (5, 5) Try to pick ordered pairs at the extremes of the = = =

2. Using y = ax + b , solve to find b. Pick one of the 2 = −4 + b ordered pairs to 2 = − + b use with the b = 3.33

3. Write out your line of best fit.

y = x + 3.33

Ex2) Find the line of best fit for the relationship between the total fat and total calories for various sandwiches. Use the graph to the right.

1. Pick two points on the line and find the slope between them.

Slope: (0, 200) & (34, 585)

= .

2. Using y = ax + b , solve to find b. 200 = 11.32(0) + b b = 200

3. Write out your line of best fit.

y = 11.32x + 200

4. Now let’s use the calculator to determine the actual line of best fit equation as well as the value of r.

5 9 13 20 21 25 28 30 31 34 y = 11.63x + 195.21 300 260 320 440 420 500 560 530 550 585 These are the ordered pairs I used to find the function. Practice (round to the nearest hundredth): 1. Using the data in the table, find the equation of the line of best fit using a calculator.

x -4 -3 -1 0 4 9 y -2 -1 0 4 5 8 y = 0.77x + 1.69

2. Describe the correlation between the data above. Find the correlation coefficient, r, using a calculator.

Positive correlation; r = 0.95

3. A student who waits on tables at a restaurant recorded the cost of meals and the tip left by single diners.

Meal Cost $4.75 $6.84 $12.52 $20.42 $8.97

Tip $0.50 $0.90 $1.50 $3.00 $1.00

If the next diner orders a meal costing $10.50, how much tip should the waiter expect to receive?

Equation: y = 0.16x – 0.30 Tip expected: $1.38

4. The table below gives the number of hours spent studying for a science exam (x) and the final exam grade (y).

x 2 5 1 0 4 2 3 Y 77 92 70 63 90 75 84

Predict the exam grade of a student who studied for 6 hours.

Equation: y = 6.1x + 63.93 Grade expected: 100.53%

**Does this even make sense?? Sometimes best fit lines give false predictions!