Analyzing Residuals Assignment and Quiz 80%

George Box, a famous statistician, once said, "All models are wrong, but some are useful." What did George Box mean by this statement?

A model is an estimate or approximation of a data set. In the real world, there are too many variables to know exactly what will happen. However, if a model is a good fit, then it can be used to make predictions about what will happen. With a useful model, a predicted value should be a good estimate of an observed value.

For the given table, which point lies on the residual plot? (1, 26) (2, 18.3) (3, 4.6) (4, 19)

(3, 4.6)

Points and their residual values are shown in the table. Which point is farthest from the line of best fit?( , )

(3,6.2)

Consider the table showing the given, predicted, and residual values for a data set. Which point would be on the residual plot of the data? (1, -1.6) (2, 1.5) (3, 4.5) (4, -0.6)

(4, -0.6)

Consider the table showing the given, predicted and residual values for a data set. Which point would be on the residual plot of the data? (1, -2.2) (2, 1.5) (3, 3.7) (4, 0.1)

(4, 0.1)

The line of best fit to model the data in the table is y = 5.2x - 0.4. What is the residual for 5? -1.6 -0.6 0.6 1.6

-1.6

Kiley gathered the data in the table. She found the approximate line of best fit to be y = 1.6x - 4. What is the residual value when x = 3? -1.8 -0.2 0.2 1.8

-1.8

The predicted values were computed by using the line of best fit, y = 3.2x + 2. What are the residual values needed to complete the chart? a = b = c = d =

0.9 -1 -0.6 0.2

Consider the graph of the line of best fit, y = 0.5x + 1, and the given data points. Which is the residual value when x = 2? -2 -1 1 2

NOT: 2

Points and their residual values are shown in the table. Which residual value is the farthest from the line of best fit? 0.19 0.7 2 8

NOT: 2

Consider the plot that was created from the residuals of a line of best fit for a set of data. Does the residual plot show that the line of best fit is appropriate for the data? Yes, the points are rising. Yes, the points are all above the x-axis. No, it follows a pattern. No, the points are falling.

No, it follows a pattern.

Find the residual values, and use the graphing calculator tool to make a residual plot. Does the residual plot show that the line of best fit is appropriate for the data? No, the points are in a curved pattern. No, the points are evenly distributed about the x-axis. Yes, the points are in a linear pattern. Yes, the points have no pattern.

No, the points are in a curved pattern.

Consider the plot created from the residuals of a line of best fit for a set of data. Does the residual plot show that the line of best fit is appropriate for the data? Yes, the points have no pattern. Yes, the points are evenly distributed about the x-axis. No, the points are in a linear pattern. No, the points are in a curved pattern

No, the points are in a linear pattern.

What does a residual value of -4.5 mean in reference to the line of best fit? The data point is 4.5 units above the line of best fit. The data point is 4.5 units below the line of best fit. The line of best fit is not appropriate to the data. The line of best fit has a slope of -4.5.

The data point is 4.5 units below the line of best fit.

Which statements describe a residual plot for a line of best fit that is a good model for a scatterplot? Check all that apply. There are about the same number of points above the x-axis as below it. The points are randomly scattered with no clear pattern. The points lie on a line. The points lie on a curve. The number of points is equal to those in the scatterplot. The y-coordinates of the points are the same as the points in the scatterplot.

There are about the same number of points above the x-axis as below it. The points are randomly scattered with no clear pattern. The number of points is equal to those in the scatterplot.

Find the residual values, and use the graphing calculator tool to make a residual plot. A 4-column table with 5 rows. The first column is labeled x with entries 1, 2, 3, 4, 5. The second column is labeled given with entries 3.5, 2.3, 1.1, negative 2.2, negative 4.1. The third column is labeled predicted with entries 4.06, 2.09, 0.12, negative 1.85, negative 3.82. The fourth column is labeled residual value with all entries blank. Does the residual plot show that the line of best fit is appropriate for the data? Yes, because the points have no clear pattern. No, the points have no pattern. No, the points are in a linear pattern. Yes, the points are in a curved pattern.

Yes, because the points have no clear pattern.

Which table of values represents the residual plot?

a

Miguel wrote the predicted and residual values for a data set using the line of best fit y = 1.82x - 4.3. He left out two of the values. A 4-column table with 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled given with entries negative 2.3, negative 0.9, 1.1, 3.1. The third column is labeled predicted value with entries negative 2.48, negative 0.66, a, 2.98. The fourth column is labeled residual value with entries 0.18, negative 0.24, negative 0.06, b. Which represents the missing values of a and b? a = 1.16 and b = 0.12 a = 1.16 and b = -0.12 a = 0.5 and b = 6.08 a = 0.5 and b = -6.08

a = 1.16 and b = 0.12

A scatterplot consists of (1, 4.0), (2, 3.3), (3, 3.8), (4, 2.6), and (5, 2.7). The line of best fit used to model the data is y = -0.33x + 4.27. Which residual plot is correct?

b