Chapter 10: Linear Regression and Correlation
Chapter 10 Review
Chapter Review from 10.1
The most basic type of association is a linear association. This type of relationship can be defined algebraically by the equations used, numerically with actual or predicted data values, or graphically from a plotted curve. (Lines are classified as straight curves.) Algebraically, a linear equation typically takes the form y = mx + b, where m and b are constants, x is the independent variable, y is the dependent variable. In a statistical context, a linear equation is written in the form y = a + bx, where a and b are the constants. This form is used to help readers distinguish the statistical context from the algebraic context. In the equation y = a + bx, the constant b that multiplies the x variable (b is called a coefficient) is called the slope. The slope describes the rate of change between the independent and dependent variables; in other words, the rate of change describes the change that occurs in the dependent variable as the independent variable is changed. In the equation y = a + bx, the constant a is called the y-intercept. Graphically, the y-intercept is the y coordinate of the point where the graph of the line crosses the y axis. At this point x = 0.
The slope of a line is a value that describes the rate of change between the independent and dependent variables. The slope tells us how the dependent variable (y) changes for every one unit increase in the independent (x) variable, on average. The y-intercept is used to describe the dependent variable when the independent variable equals zero. Graphically, the slope is represented by three line types in elementary statistics.
Formula Review
y = a + bx where a is the y-intercept and b is the slope. The variable x is the independent variable and y is the dependent variable.
Use the following information to answer the next three exercises. A vacation resort rents SCUBA equipment to certified divers. The resort charges an up-front fee of 💲25 and another fee of 💲12.50 an hour.
What are the dependent and independent variables?
Solution
dependent variable: fee amount; independent variable: time
Find the equation that expresses the total fee in terms of the number of hours the equipment is rented.
Graph the equation from [link].
Solution
Use the following information to answer the next two exercises. A credit card company charges 💲10 when a payment is late, and 💲5 a day each day the payment remains unpaid.
Find the equation that expresses the total fee in terms of the number of days the payment is late.
Graph the equation from [link].
Solution
Is the equation y = 10 + 5x – 3x2 linear? Why or why not?
Which of the following equations are linear?
a. y = 6x + 8
b. y + 7 = 3x
c. y – x = 8x2
d. 4y = 8
Solution
y = 6x + 8, 4y = 8, and y + 7 = 3x are all linear equations.
Does the graph show a linear equation? Why or why not?
[link] contains real data for the first two decades of AIDS reporting.
| Year | # AIDS c