The correlation between temperature in ◦F and age in weeks was r = −0.70. If we converted the temperature to ◦C and age to months, what would the 29 correlation be?

Question

The correlation between temperature in ◦F and age in weeks was r = −0.70. If we converted the temperature to ◦C and age to months, what would the 29 correlation be?

BlackTom AI · Accepted Answer

When both variables are transformed by linear, positive-slope conversions, the correlation coefficient r remains the same in magnitude and preserves its sign.

Option 1: 'the absolute value of r will increase.' This would imply a stronger linear relationship after converting units, which is not the case for standard linear unit conversions (Fahrenheit to Celsius and weeks to months) since these are simply scaling and shifting with positive slopes. The strength of the linear relationship (|r|) stays the same.

Option 2: '-0.70' This matches the principle that r is invariant under positive linear transformations of the variables. Converting temperature from F to C uses a = 5/9 > 0 and b = -32, and converting age from weeks to months also uses a positive scaling. Therefore the correlation coefficient keeps its magnitude and sign.

Option 3: 'the absolute value of r will decrease.' This would suggest a weakening of the linear association after unit changes, which contradicts the mathematical property that positive linear transformations do not change |r|.

Option 4: '+0.70' This would indicate a reversal of the direction of the relationship (a positive association) after the conversions, but since all transformations are with positive slopes, the sign of r should remain negative rather than flip to positive.

In summary, because the unit conversions are linear and with positive slopes, the correlation coefficient remains exactly -0.70.

FA25_QTM_100_3 8.12: Crawling babies, Part I. - Requires Respondus LockDown Browser

The correlation between temperature in ◦F and age in weeks was r = −0.70. If we converted the temperature to ◦C and age to months, what would the 29 correlation be?

查看解析

登录即可查看完整答案

类似问题

Of the following, the correlation coefficient that indicates the weakest relationship between the two variables being measured is ______________.

The correlation in between mobile usage and exam score of a person found to be -2.2. What is your inference from the above statement.

Their correlation coefficients will be the same, since the correlation coefficient is unitless.

r = −0.85

r = −0.03

r = −0.48

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单