Transformations to Achieve Linearity

• Model A is appropriate, since the relationship between x and y is linear.

• Model B is appropriate, since the relationship between x and y is linear.

• Model A is appropriate, since the relationship between log x and log y is linear.

• Model A is appropriate, since the relationship between log x and y is linear.

• Model B is appropriate, since the relationship between x and log y is linear.

Curved relationships between two quantitative variables can sometimes be changed into linear relationships by __________________ one or both of the variables. Once we transform the data to achieve linearity, we can fit a least-squares regression line to the transformed data and use this linear model to make predictions.

Another useful strategy for straightening a curved pattern in a scatterplot is to take the ___________________ of one or both variables. When a power model describes the relationship between two variables, a plot of log y versus log x (or ln y versus ln x) should be linear.

True or False: Linear transformations can straighten a curved relationship between two variables.

• True

• False

The linear parent function, f(x) = x, is transformed to g(x) = f(x) - 6. Describe the transformation. (a)  

• g(x) is shifted up 6 units

• g(x) is shifted down 6 units

• g(x) is shifted left 6 units

• g(x) is shifted right 6 units

What is the effect on the graph of the linear parent function, f(x) = x, when f(x) is replaced by f(x- 7)? Complete the sentence by selecting the correct answers from the drop-down menus. The graph of the line ​ (a)   ​ ​ (b)   7 units.

• shifts horizontally

• up

• down

• left

• right

• shifts vertically

Rewrite f(x) = 2x - 1 shifted up three units and the slope doubled (a)  

• f(x) = 5x - 2

• f(x) = 4x + 2

• f(x) = 4x + 3

• f(x) = 5x - 4

When theory or experience suggests that the relationship between two variables follows a ___________ ___________ of the form y=ax^p, transformations involving powers and roots can linearize a curved pattern in a scatterplot.