Lesson 4 Rocking the Residuals Solidify Understanding

Ready

1.

Interpret the data provided in the box plot for the first quiz of a unit of study for a group of math students.

Quiz 1 scores: A box plot with the left whisker beginning at 0 and extending to 2 where the left box begins. The left box ends at 2.5 where the right box begins. The right box ends at 3.5, where the right whisker begins. The right whisker ends at 4. 0.50.50.51111.51.51.52222.52.52.53333.53.53.5444000Quiz 1 Scores

What is the median score?

What is the range?

Did students do well on the quiz?

2.

Interpret the data provided in the box plot for the second quiz of a unit of study for a group of math students.

Quiz 2 scores: A box plot with the left whisker beginning at 1 and extending to 2 where the left box begins. The left box ends at 3 where the right box begins. The right box ends at 4. There is not a right whisker. 1111.51.51.52222.52.52.53333.53.53.5444Quiz 2 Scores

What is the median score?

What is the range?

Did students do well on the quiz?

3.

Look back at the box plots for problems 1 and 2. Which quiz did students perform better on the first quiz or the second quiz? Why?

Data is often collected using a survey with several questions. Questions that need to be answered with a number generate numerical data. Questions that produce responses that are not numbers generate categorical data.

Determine whether the questions in the following problems create numerical data or categorical data.

4.

What is your shoe size?

A.

numerical data

B.

categorical data

5.

What is the color of your eyes?

A.

numerical data

B.

categorical data

6.

What type of pet do you have?

A.

numerical data

B.

categorical data

7.

How tall are you?

A.

numerical data

B.

categorical data

8.

Where is your favorite place to visit?

A.

numerical data

B.

categorical data

9.

How many siblings do you have?

A.

numerical data

B.

categorical data

Set

The data sets in problems 10 and 11 are scatterplots that have the regression line and the residuals marked. For each exercise, use the given data set to create a residual plot, and then assess the fit of the linear function to the data based on the residuals.

10.

Data Set 1

A scatterplot with the regression line and the residuals marked. The independent variable and the approximate residuals are: [2, -3], [4, 4], [7, -3], [9, 0], [16, 1] x555101010151515y101010202020303030000

Residual Plot 1

A blank coordinate plane with horizontal axis extending from 0 to 19 and vertical axis extending from -14 to 14. x555101010151515y–10–10–10101010000

11.

Data Set 2

A scatterplot with the regression line and the residuals marked. The independent variable and the approximate residuals are: [3, 0.5], [4, 2], [5, -1], [7, -2.5], [8, -1], [9, -1.5], [10, 3] x000555101010y303030353535404040454545505050555555

Residual Plot 2

A blank coordinate plane with horizontal axis extending from 0 to 11 and vertical axis extending from -9 to 8. x555101010y–5–5–5555000

12.

Consider the residual plot below, determine whether the regression line is a good fit to the data or not, and then explain why it is or is not a good fit.

A residual plot of 11 points at approximately (0, 0.4), (5, 0.2), (6, 0.1), (7, -0.2), (8, -0.3), (9, -0.4), (10, -0.6), (11, -0.7), (12, -0.4), (13, 3.3), (14, -1.2) x444555666777888999101010111111121212131313141414y–1–1–1000111222333

13.

Consider the residual plot below, determine whether the regression line is a good fit to the data or not, and then explain why it is or is not a good fit.

A residual plot of 13 points at approximately (440, -2.9), (460, 3.9), (480, 4.5), (485, - 5.6), (520, 0.2), (520, -3.5), (560, 5), (580, 0.8), (625, - 3), (650, - 0.6), (675, -0.1), (714, 2.5), (730, -1) x350350350400400400450450450500500500550550550600600600650650650700700700750750750y–6–6–6–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1000111222333444555

Decide if you agree or disagree with the following statements, and explain why.

14.

By analyzing the residuals, the quality of fit between a function and the data can be determined.

15.

When bivariate data have a strong correlation, that means that one of the data items causes the other item.

Go

Use technology to compute the correlation coefficient for a linear regression equation for each set of data. Then interpret the correlation coefficient, and describe the nature of the data in terms of the fit to a linear model.

16.

Shoe Size

Height (inches)

17.

Absences at school

Scored on Test

18.

Number of Visitors to Store

Number of Sales Transactions

19.

Games Played

Points Scored per Game