1 of 8 0-day streak

Fit and write a transformed least-squares equation

Question 1 of 8

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The explanatory variable is input setting (units), symbol i; the response variable is signal power (mW), symbol P. Fit after applying the reciprocal to the response variable only. Calculate the least-squares intercept a and slope b from the displayed raw observations. Report coefficients to 2 decimal places, retaining unrounded values for any residual calculation

Use the displayed 7-case data to fit a least-squares line after transforming the response variable with a reciprocal

input setting (units)	signal power (mW)
3	6
4	7
5	8
6	9
7	10
8	11
9	12

(a)1 mark

Which pair of lists should be used for the regression?

unchanged input setting as x; reciprocal of signal power as y

unchanged input setting as x; unchanged signal power as y

transformed signal power as x; unchanged input setting as y

reciprocal of input setting as x; unchanged signal power as y

(b)2 marks

Use your computed fit to record intercept a and slope b to 2 decimal places in the labelled fields

These displayed coefficients report the fit; full technology values are retained for any later residual calculation

\(a\) \(b\)

Calculate the transformed fit from the displayed raw observations. Which equation uses the declared variable symbols and coefficients rounded to 2 decimal places?

\widehat{\frac{1}{P}}\approx -0.01 + 0.20i

\widehat{i}\approx 14.32 - 70.99\frac{1}{P}

\widehat{\frac{1}{P}}\approx 0.20 - 0.01i

\widehat{P}\approx 0.20 - 0.01i

\widehat{P}\approx 0.20 - 0.01\frac{1}{i}