1 of 8 0-day streak

Residuals and what least squares minimises

Question 1 of 8

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The data use time since watering as the explanatory variable and soil moisture reading as the response variable

Let \(x\) represent time since watering in min, and let \(y\) represent soil moisture reading in sensor units. The fitted line is:

y = 181 - x

The stated data point is (38, 146), with the explanatory value first

(a)1 mark

Calculate the signed residual for the data point (38, 146)

Residual for (38, 146) (sensor units)

(b)1 mark

Which statement gives the quantity that the least squares method minimises?

For these 10 cases, least squares minimises the number of non-zero vertical residuals from the fitted line

For these 10 cases, least squares minimises the sum of the squared vertical residuals from the fitted line

For these 10 cases, least squares minimises the mismatch between the fitted line's slope and the data's rise

For these 10 cases, least squares minimises the sum of the signed vertical residuals from the fitted line