University:
High School
Course:
High School Mathematics
Academic year:

2022
Views:

317

Pages:

2
Author:

eyamia6fx

Scatter Plots & Line of Fit Core Concepts Scatter Plot A scatter plot is a graph that shows the relationship between two data sets. The two data sets are graphed as ordered pairs in a coordinate plane. Scatter plots can show trends in the data. Correlation Positive Correlation: As one variable increases, the other variable also increases. Negative Correlation: As one variable increases, the other variable decreases. No Correlation: There is no apparent relationship between the two variables. Line of Fit Is an equation/line that best describes the relationship between two variables. Using a Line of Fit to Model Data from a given table Step 1 Make a scatter plot of the data. Step 2 Decide whether the data can be modeled by a line. Age and Vehicles Owned: No correlation, so there is no line of fit. Temperature and Coat Sales: Negative Correlation Step 3 Draw a line that appears to fit the data closely. There should be approximately as many points above the line as below it. Step 4 Write an equation using two points on the line. The points do not have to represent actual data pairs, but they must lie on the line of fit. A) Find slope Δy/Δx = (y2 - y1) / (x2 - x1) = (60 - 10) / (35 - 70) = 50 / -35 = -10/7 B) Make Equation y - y1 = m(x - x1) y - 60 = -10/7(x - 35) y - 60 = -10/7x + 50 y = -10/7x + 110 1. The scatter plot shows the weights (in pounds) of a baby over time. a. What is the weight of the baby when the baby is four 1 months old? 14 pounds b. What is the age of the baby when the baby weighs 17.2 pounds? 8 months old c. What tends to happen to weight of the baby as the age increases? The weight of the baby tends to increase as the age increases. In Exercises 2-5, tell whether x and y show a positive, a negative, or no correlation. 2. Positive 3. Negative 4. No correlation 5. Positive 6. The table shows the depth y (in centimeters) of water filling a bathtub after x minutes. a. Write an equation that models the depth of the water as a function of time. Time (minutes), x | 0 | 2 | 4 | 6 | 8 | 10 | 12 ---|---|---|---|---|---|---| Depth (centimeters), y | 6 | 8 | 11 | 14 | 17 | 20 | 24 Slope: (8-14)/(2-12) = -6/-10 = 3/5 y-intercept: y - 24 = 3/5(x - 12) y - 24 = 3/5x - 36/5 y = 3/5x + 96/5 = 3/5x + 19.2 b. Interpret the slope and y-intercept of the line of fit. Slope: For every 5 minutes, the water rises 8 cm. y-intercept: The bathtub started with 4 cm of water.