MAT 150 Algebra – Class #6 Topics: Find exact Linear Models for data

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Presentation transcript:

MAT 150 Algebra – Class #6 Topics: Find exact Linear Models for data Determine if a set of data can be modeled exactly or approximately Scatter Plots Linear Model = good fit? Solve Problems using Linear Models

Fitting Lines to Data Ex 1: Linear Correlation Which graph(s) has Positive Linear Correlation? Constant Correlation? Negative Linear Correlation? No Correlation? Correlation that is not Linear?

Construct a scatter plot of the data in the table Determine if the points plotted fit exactly or only approximately by a linear function. How do you know? Create a linear model for the data in the table How do you know something is linear? Use the rounded function y = f(x) that was found above to evaluate f(8) and f(11). X 1 2 3 5 7 9 12 Y 6

Earnings & Gender Education Attainment Average Annual Earnings of Males ($ in thousands) Average Annual Earnings of Females ($ in thousands) Less than ninth grade 21.659 17.659 Some high school 26.277 19.162 High School Graduate 35.725 26.029 Some College 41.875 30.816 Associate’s degree 44.404 33.481 Bachelor’s degree 57.220 41.681 Master’s degree 71.530 51.316 Doctorate degree 82.401 68.875 Professional degree 100.000 75.036

Let x represent the earnings for the males, let y represent earnings for females, and create a scatterplot on your graphing calculator of the data. Decide if there is a linear correlation. If so, create a linear model that expresses the female earnings (y) as a function of male (x) annual earnings. Graph the linear function and the data points on the graphing calculator.

According to this model, what amount would a female make if the average male with the same education made $90, 568? According to this model, what amount would a male make if the average female with the same education made $64,910? Is there another way you could have answered the previous two questions?

Population (millions) U.S. Population Use the table to estimate the population in 2002 and 2014. Be very careful about your “year 0” Year Population (millions) 1960 180.671 1995 263.044 1965 194.303 1998 270.561 1970 205.052 2000 281.422 1975 215.973 2003 294.043 1980 227.726 2025 358.030 1985 238.466 2050 408.695 1990 249.948

Assignment Pg. 121-123 #1- 4all #15-18 all #38 #45 NOTE: First Exam will be September 6. Covers both Chapters 1 and 2.