Example 2: Finding the Least-Squares Line The table shows populations and numbers of U.S. Representatives for several states in the year 2000.

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Presentation transcript:

Example 2: Finding the Least-Squares Line The table shows populations and numbers of U.S. Representatives for several states in the year 2000. State Population (millions) Representatives AL 4.5 7 AK 0.6 1 AZ 5.1 8 AR 2.7 4 CA 33.9 53 CO 4.3

Example 2 Continued A. Find an equation for a line of best fit. Use your calculator. To enter the data, press STAT and select 1:Edit. Enter the population in the L1 column and the number of representatives in the L2 column. Then press STAT and choose CALC. Choose 4:LinReg(ax+b) and press ENTER. An equation for a line of best fit is y ≈ 1.56x + 0.02. y = 1.56x + 0.02

Example 2 Continued A. Find an equation for a line of best fit. Use your calculator. To enter the data, press STAT and select 1:Edit. Enter the population in the L1 column and the number of representatives in the L2 column. Then press STAT and choose CALC. Choose 4:LinReg(ax+b) and press ENTER. An equation for a line of best fit is y ≈ 1.56x + 0.02. y = 1.56x + 0.02

Example 2 Continued B. Interpret the meaning of the slope and y-intercept. Slope: for each 1 million increase in population, the number of Representatives increases by 1.56 million y-intercept: a state with a population of 0 (or less than a million) has 0.02 Representatives (or 1 Representative). C. Michigan had a population of approximately 10.0 million in 2000. Use your equation to predict Michigan’s number of Representatives. 16

Check It Out! Example 2 The table shows the prices and the lengths in yards of several balls of yarn at Knit Mart. a. Find an equation for a line of best fit. y ≈ 0.04x + 6.38

Check It Out! Example 2 Continue b. Interpret the meaning of the slope and y-intercept. Slope: cost is $0.04 yd y-intercept: $6.38 is added to the cost of every ball of yarn c. Knit Mart also sells yarn in a 1000-yard ball. Use your equation to predict the cost of this yarn.

Check It Out! Example 2 Continue y  0.04x + 6.38 y  0.04(1000) + 6.38 y  $46.38 The average cost of 1000 yards of yarn is $46.38.

Additional Example 3: Correlation Coefficient The table shows a relationship between points allowed and games won by a football team over eight seasons. Year Points Allowed Games Won 1 285 3 2 310 4 301 186 6 5 146 7 159 170 8 190

Additional Example 3 Continued Find an equation for a line of best fit. How well does the line represent the data? Use your calculator. Enter the data into the lists L1 and L2. Then press STAT and choose CALC. Choose 4:LinReg(ax+b) and press ENTER. An equation for a line of best fit is y ≈ –0.02x + 9.91. The value of r is about –0.91, which represents the data very well.