For a straight line $y = a + bx$ fitted by least squares, which of the following are true?
I. It makes the sum of the squared vertical distances from the points as small as possible.
II. The deviations of the actual values from the trend values add up to 0.
III. It passes through the point $(\bar{x}, \bar{y})$ .
IV. Its slope $b$ is always positive.

All four: I, II, III and IVCorrect answerYour answerI and II onlyCorrect answerYour answerII and III onlyCorrect answerYour answerI, II and III onlyCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

I is what 'least squares' means. II and III follow from the first normal equation, $\sum y = na + b\sum x$ .
IV is false: a falling series gives a negative slope.

Concept: Properties of the least-squares line
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsA straight-line trend by least squares

Practise this chapter →

Ten questions from Time Series & Trend, at your own pace.

Explanation