4-5 Scatter Plots and Lines of Best Fit Goals: Write a linear equation that approximates a set of data points Determine if there is a positive, negative or no correlation between data points. Eligible Content: A1.1.2.1.1 / A1.1.2.1.3 / A1.2.2.1.3 / A1.2.2.2.1 / A1.2.3.2.1 / A1.2.3.2.2 / A1.2.3.2.3

Vocabulary Data – collection of numbers or pairs of numbers to be analyzed. Scatterplot - a graph of pairs of numbers that represent a real-life situation.

Scatterplot

Vocabulary Best Fitting Line - line that is the best approximation of where the points lie. Other terms for Best Fitting Line: Line of Best Fit Regression Line Trend Line

Vocabulary Correlation – the relationship between the inputs and the outputs. Other term for correlation: Trend Types of correlation: Positive Negative No Correlation

Positive Correlation Line of best fit has a positive slope Points are increasing from left to right

Negative Correlation Line of best fit has a negative slope Points are decreasing from left to right

Relatively No Correlation Line of best fit cannot be drawn Points are scattered

Example The graph shows the average number of students per computer in Maria’s school. Determine whether the graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, describe its meaning in the situation. The graph shows a negative correlation. Each year, more computers are in Maria’s school, making the students-per-computer rate smaller.

The graph shows the number of mail-order prescriptions The graph shows the number of mail-order prescriptions. Determine whether the graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, describe it. A. Positive correlation; with each year, the number of mail-order prescriptions has increased. B. Negative correlation; with each year, the number of mail-order prescriptions has decreased. C. no correlation D. cannot be determined

How to find the Equation of the Line of Best Fit Draw the scatter plot of the data. Sketch the line of best fit. Pick 2 points on the line. Find the slope. Find the y-intercept. Write the equation of the line.

Write an equation of your line. Approximating a Best-Fitting Line Years since 1900 Distance (ft) 8 16 24 32 40 48 56 64 72 80 88 96 104 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 DISCUS THROWS The winning Olympic discus throws from 1908 to 1996 are plotted in the graph. Approximate the best-fitting line for these throws. Write an equation of your line.

Approximating a Best-Fitting Line Years since 1900 Distance (ft) 8 16 24 32 40 48 56 64 72 80 88 96 104 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 SOLUTION (96, 230). (96, 230) Find two points that lie on the best-fitting line, such as (8, 140) and (96, 230). (8, 140) Find the slope of the line through these points.

m = y = m x + b y = m x + b 140 = (1.02) (8) + b 140 for y. Approximating a Best-Fitting Line Years since 1900 Distance (ft) 8 16 24 32 40 48 56 64 72 80 88 96 104 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 (96, 230) (8, 138) y2 – y1 x2 – x1 m = 230 – 140 96 – 8 = 90 88 1.02 230 – 138 96 – 8 = y = m x + b Write slope intercept form. Substitute 1.05 for m, 8 for x, 140 for y. 140 = (1.02) (8) + b 92 88 = 1.05 y = m x + b 140 = 8.16 + b Simplify. 131.84 = b Solve for b. An equation of the best-fitting line is y = 1.02 x + 131.84. In most years, the winner of the discus throw was able to throw the discus farther than the previous winner.

Example The table shows the amount of sleep a baby needs at each age. Make a scatter plot of the data and find the equation of the line of best fit. Age (weeks) Sleep (hours) 3 15.8 6 15.1 14 15.4 18 15.2 27 14.4 39 14.2 45 13.9 47 13.1 49 13.7 50 13.2 y = -0.05 x + 15.85

Practice The table shows the largest vertical drops of nine roller coasters in the US and the number of years after 1988 that they were opened. Make a scatterplot and find the equation of the line of best fit. y = 15x + 120 Years since 1988 1 3 5 8 12 13 15 Vertical drop (feet) 151 155 225 230 306 300 255 400

Homework Pages 250-251 #1-7 for #3 only complete parts a-c.