AP Stats Transforming Linear Data Test Review

True or False: Applying a function such as the logarithm or square root to a quantitative variable is called transforming the data.

• True

• False

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

• True

• False

Tags

CCSS.HSF-LE.A.1B

Check all that can be represented by a power model.

• The distance that an object dropped from a given height falls is related to time since release

• The time it takes a pendulum to complete one back-and-forth swing (its period) is related to its length

• The intensity of a light bulb is related to distance from the bulb

True or False: If a variable grows exponentially, its logarithm grows linearly.

• True

• False

Tags

CCSS.HSF.BF.B.5

When choosing between different models to describe a relationship between two quantitative variables (select all that apply):

• If there is more than one model with a randomly scattered residual plot, choose the model with the largest coefficient of determination, r².

• use the standard deviation of the residuals to help choose a model, as the y values for the different models might be on different scales

• Choose the model whose residual plot has the most random scatter.

Tags

CCSS.HSS.ID.B.6B

Curved relationships between two quantitative variables can sometimes be changed into linear relationships by (a)   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.

Tags

CCSS.HSF-LE.A.1B

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.

(a)  

Tags

CCSS.HSS.ID.B.6

Another useful strategy for straightening a curved pattern in a scatterplot is to take the (a)   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.

For an ___________________ ___________ of the form y=ab^x, the predicted values of the response variable are multiplied by a factor of b for each increase of 1 unit in the explanatory variable. When an exponential model describes the relationship between two variables, a plot of log y versus x (or ln y versus x) should be linear.

(a)  

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

CCSS.HSF.LE.A.4

To decide between competing models, choose the model with the most (a)   scattered residual plot.

Tags

CCSS.HSS.ID.B.6B