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Chapter 10: Q3BSC (page 468)

a. What is a residual?

b. In what sense is the regression line the straight line that 鈥渂est鈥� fits the points in a scatterplot?

Short Answer

Expert verified

a. A residual represents the difference between the observed and predicted value of the dependent variable (y).

b. The regression line is the best fit as it describes the linear association between variables such that it has the minimum possible error.

Step by step solution

01

Define the term residual

a.

A residual is the difference between two values obtained for a value of the independent variable;observed and predicted value of the dependent variable y at x. Mathematically it is computed as,

\(\begin{array}{c}Residual = observed\;y - predicted\;y\\ = y - \hat y\end{array}\)

02

Discuss that the regression line is best fit.

b.

A regression line is obtained as the straight line which describes the relationship between a set of variables such that it has the lowest possible error.

The property of the regression line, that thesum of squares of the residuals is the lowest possible sum, makes it the best fit straight line.

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Pain Intensity Before Duragesic Treatment

1.2

1.3

1.5

1.6

8

3.4

3.5

2.8

2.6

2.2

3

7.1

2.3

2.1

3.4

6.4

5

4.2

2.8

3.9

5.2

6.9

6.9

5

5.5

6

5.5

8.6

9.4

10

7.6










Pain Intensity After Duragesic Treatment

0.4

1.4

1.8

2.9

6

1.4

0.7

3.9

0.9

1.8

0.9

9.3

8

6.8

2.3

0.4

0.7

1.2

4.5

2

1.6

2

2

6.8

6.6

4.1

4.6

2.9

5.4

4.8

4.1










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