Section 6.2 Linear Regression

Text of section.

Exercises Exercises

1.

A survey of local companies collects information about marketing budgets \(X\) and revenue \(Y\) (each measures in thousands of dollars), shown below. A linear regression gives the best linear fit as \(Y = 18.28 X + 29.69\text{.}\) What is the coefficient of determination \(r^2\text{?}\)

Table 6.2.1.

\(x_i\)	\(y_i\)	\((y_i - \text{avg})^2\)	\(\text{pred } y_i\)	\(\text{res}^2\)
200	4300	2073600	3686	377377
420	7700	3841600	7707	53
270	4500	1537600	4965	216495
380	7000	1587600	6976	572
300	5200	291600	5514	98401
sum:	28700	9332000	28848	692898

2.

A sample of 100 measurements are taken and a best fit line is calculated, resulting in the data below (the final line shows the sums for each column). Find the coefficient of determination.

Table 6.2.2.

\(x_i\)	\(y_i\)	\(\text{pred } y_i\)	\((y - \text{avg})^2\)	\(\text{res}^2\)
38.00	121.00	93.17	11.83	774.33
87.00	241.00	238.95	13586.23	4.22
30.00	61.00	69.37	4024.63	70.12
35.00	85.00	84.25	1555.51	0.57
⋮	⋮	⋮	⋮	⋮
33.00	108.00	78.30	270.27	882.19
26.00	32.00	57.47	8545.15	648.91
sum:	12444.00	12444.00	515206.64	29789.80

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