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Chapter 3: Q. 56 (page 193)

56. Do heavier people burn more energy? Refer to Exercise54.
(a) Use your calculator to make a residual plot. Describe what this graph tells you about how well the line fits the data.
(b) Which point has the largest residual? Explain what the value of that residual means in context.

Short Answer

Expert verified

(a) The data does not appear to have an obvious pattern, the regression line appears to be a decent fit for the data.

(b) The point with the largest residual is (42,1418).

Step by step solution

01

Part (a) Step 1: Concept introduction 

A residual plot is a graphic tool for determining the relationship between a transmitted independent variable and the retort variable when multiple independent variables are used.

02

Part (a) Step 2: Explanation 

The difference between the actual and expected values called the residual. The horizontal axis contains the mass, and the vertical axis contains the residuals.

03

Part (b) Step 1: Concept introduction 

In statistics, residual values direct the portion of the variability in a dependent variable fragment that is left after the forecasters have accounted for the variability described in the investigation.

04

Part (b) Step 2: Explanation 

The table shows the values of predicted and residuals:

Mass (kg)
(X)
Metabolic rate (cal/24hrs)
(Y)
Predicted Y
(Y)
Residuals
(Y-Y)
36.1
995
1068.503
-73.5026
54.6
1425
1512.985
-87.9848
48.5
1396
1366.426
29.57417
42
1418
1210.256
207.7436
50.6
1502
1416.881
85.11943
42
1256
1210.256
45.7436
40.3
1189
1169.412
19.58792
33.1
913
996.4244
-83.4244
42.4
1124
1219.867
-95.8668
34.5
1052
1030.061
21.9391
51.1
1347
1428.894
-81.8936
41.2
1204
1191.036
12.96446

From the above table, the point (42,1418)has the largest residual. Hence, the point deviate greatly from a line, it is an outlier.

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