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Fit and write a transformed least-squares equation

Question 1 of 8

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The explanatory variable is dose (mg), symbol x; the response variable is response index (units), symbol z. Fit after applying the reciprocal to the explanatory 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

The table records dose and response index for 5 cases. A reciprocal transformation is applied to the explanatory variable before fitting a least-squares line

response index (units)	dose (mg)
30	2
43	3
44	4
51	5
50	6

(a)1 mark

Which technology input matches the stated one-axis transformation?

reciprocal of dose as x; unchanged response index as y

unchanged dose as x; unchanged response index as y

unchanged response index as x; transformed dose as y

unchanged dose as x; reciprocal of response index 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{z}\approx 61.41 - 61.41x

\widehat{\frac{1}{x}}\approx 0.96 - 0.02z

\widehat{z}\approx 61.41 - 61.41\frac{1}{x}

\widehat{z}\approx -61.41 + 61.41\frac{1}{x}

\widehat{\frac{1}{z}}\approx 61.41 - 61.41x