A study on the oxygen consumption rate (OCR) of sea cucumbers involved random samples of size 3 at each of the temperatures 10, 11, 12, 13, 14, and $15 ^ { \circ } \mathrm { C }$ . A regression model was fit in order to study the
Relationship between OCR and temperature. The slope of the regression line was found to be positive.
If one of the analysts converted the temperatures to Fahrenheit $\left( { } ^ { \circ } \mathrm { F } = 32 + ( 9 / 5 ) ^ { 0 } \mathrm { C } \right)$ the slope of the
Regression line would be
A) increased by a factor $9 / 5$
B) increased by a factor $5 / 9$
C) unaltered
D) decreased by a factor $9 / 5$

Question

A study on the oxygen consumption rate (OCR) of sea cucumbers involved random samples of size 3 at each of the temperatures 10, 11, 12, 13, 14, and $15 ^ { \circ } \mathrm { C }$ . A regression model was fit in order to study the
Relationship between OCR and temperature. The slope of the regression line was found to be positive.
If one of the analysts converted the temperatures to Fahrenheit $\left( { } ^ { \circ } \mathrm { F } = 32 + ( 9 / 5 ) ^ { 0 } \mathrm { C } \right)$ the slope of the
Regression line would be 
A) increased by a factor $9 / 5$
B) increased by a factor $5 / 9$
C) unaltered
D) decreased by a factor $9 / 5$

Quizplus · Accepted Answer

Converting Celsius to Fahrenheit involves multiplying by 9/5 and adding 32. Therefore, if we convert all the temperatures in the original regression model to Fahrenheit, the OCR values will also change accordingly. The slope of the new regression line will represent the change in OCR for a change in Fahrenheit temperature, rather than Celsius temperature.

Recall that the original slope was positive, indicating that as temperature increases, so does OCR. Multiplying the change in Fahrenheit temperature by 9/5 (the conversion factor) will result in a larger increase in OCR compared to the original increase in Celsius temperature. Therefore, the slope of the new regression line will be steeper than the slope of the original regression line, indicating a greater increase in OCR per degree Fahrenheit compared to per degree Celsius.

A Study on the Oxygen Consumption Rate (OCR) of Sea 15∘C15 ^ { \circ } \mathrm { C }15∘C

A Study on the Oxygen Consumption Rate (OCR) of Sea $15 ^ { \circ } \mathrm { C }$