MA 458 | Test Review – Unit 2 (Two-Quantitative Variables)

Scatterplots and Correlation

100

What does DOFS stand for?

Direction, Outliers, Form, Strength

200

Identify the direction and strength for a correlation coefficient of r = -0.91.

Direction: negative (decreasing)

Strength: very strong

300

How do we know if a point is an outlier?

It is out of the pattern / rest of the data points.

400

What words should we say for "context," when using DOFS + context?

"the relationship between explanatory variable and response variable"

500

Identify the form for a correlation coefficient of r = 0.41.

TRICK QUESTION

You cannot identify the form (or outliers) without also being given a graph. In this situation, you would only be able to identify Direction and Strength (and maybe context).

LSRL

100

What is

\hat{y}

 called?

y-hat

200

The dependent variable is distance traveled (in cm).

                   Coefficient

Intercept        0.25

Rubberbands  3.24

Identify the y-intercept.

0.25

300

The dependent variable is distance traveled (in cm).

                   Coefficient

Intercept        0.25

Rubberbands  3.24

Identify the slope.

3.24

400

The dependent variable is distance traveled (in cm).

                   Coefficient

Intercept        0.25

Rubberbands  3.24

Identify the response variable.

distance traveled

500

The dependent variable is distance traveled (in cm).

                   Coefficient

Intercept        0.25

Rubberbands  3.24

Identify the explanatory variable.

# of rubberbands

LSRL Interpretations

100

The dependent variable is distance traveled (in cm).

                   Coefficient

Intercept        0.25

Rubberbands  3.24

Identify the equation of the LSRL, in context.

 \hat{dist}=0.25+3.24{rrbs} 

200

The dependent variable is distance traveled (in cm).

                   Coefficient

Intercept        0.25

Rubberbands  3.24

Identify the y-intercept of the LSRL, in context.

When there are 0 rubberbands, we predict the distance traveled to be 0.25 centimeters.

300

The dependent variable is distance traveled (in cm).

                   Coefficient

Intercept        0.25

Rubberbands  3.24

Identify the slope of the LSRL, in context.

For every rubberband added, we predict an increase of distance traveled by 3.24 cm.

400

Suppose r² is 0.79 and the dependent variable is distance traveled.

Interpret r², in context.

About 79% of the variability in distance traveled can be accounted for by the LSRL.

500

Suppose our model predicts distance traveled to be 45.23 cm, but the actual value for a certain number of rubberbands is 43 cm. 

Interpret the residual, in context.

Our prediction was too high by 2.23 cm (from the actual).

Choosing the Best Regression Model

100

If I want to use a scatterplot of the relationship between two quantitative variables to determine if a linear model is appropriate to use, how should the scatterplot look?

The scatterplot should show a linear relationship. 

In general, the model should "match up" with the form.

200

If I wanted to use a residual plot for two quantitative variables to determine if a model was appropriate, what should the residual plot look like?

The residual plot should have random scatter and no clear pattern.

300

If I am trying to determine which model is best and I wish to use the s, I should choose the model that has the _________ s.

Fill in the blank.

smaller

400

If I am trying to determine which model is best and I wish to use the r², I should choose the model that has the _________ r².

Fill in the blank.

greater

500

Name the three regression models that we have covered. 

1. L ______

2. Q ______

3. E ______

Linear

Quadratic

Exponential

Re-Expressing Data

100

Solve for

\hat{y}

when x = 10:

\hat{y} = 2+0.5x

 \hat{y}=7 

200

Solve for

\hat{y}

when x = 10:

\sqrt{\hat{y}} = 2+0.5x

 \hat{y}=49 

300

Solve for

\hat{y}

when x = 10:

(\hat{y})^2 = 2+0.5x

 \hat{y}=2.65 

400

Solve for

\hat{y}

when x = 10:

log(\hat{y}) = 2+0.5x

 \hat{y}=10000000 

500

Solve for

\hat{y}

when x = 10:

ln(\hat{y}) = 2+0.5ln(x)

 \hat{y}=23.37