Question Type 1: Finding regression x onto y instead of y onto x Bootcamps

Given the data points $(2,3)$, $(4,5)$, and $(6,7)$, find the regression line of $x$ on $y$.

For the points $(5,10),(10,20),(15,30),(20,40)$, determine the regression line of $x$ on $y$.

Given the data $(0,1),(1,2),(2,1),(3,3),(4,4)$, find the regression line of $x$ on $y$.

For the four points $(1,2),(2,3),(3,5),(4,4)$, determine the regression line of $x$ on $y$.

In a study, hours studied $x$ and exam score $y$ were recorded as $(2,50),(4,60),(6,65),(8,70),(10,80)$. Find the regression line of hours studied on exam score.

Find the regression line of $x$ on $y$ for the five perfectly negatively correlated points $(1,8),(2,6),(3,4),(4,2),(5,0)$.

Find the regression line of $x$ on $y$ for the six points $(2,1),(3,2),(5,3),(7,5),(9,7),(11,9)$.

For $n=10$ data points it is known that $\bar x=50$, $\bar y=30$, $\sum_{i}(y_i-30)^2=2000$ and $\sum_{i}(x_i-50)(y_i-30)=1600$. Find the regression line of $x$ on $y$.

Using summary statistics for 12 observations: $\bar x=20.5$, $\bar y=15.2$, $\sum(y_i-15.2)^2=340$, $\sum(x_i-20.5)(y_i-15.2)=255$, find the regression line of $x$ on $y$.

In an experiment the reaction rate $x$ (mol/s) and temperature $y$ (°C) were measured as $(0.05,20),(0.07,30),(0.12,40),(0.15,50),(0.20,60),(0.22,70),(0.25,80)$. Find the regression line of reaction rate on temperature.

Given eight observations of advertising spend $y$ (in $\text{k}$) and sales $x$ (in $\text{k}$): $(5,100),(10,150),(15,200),(20,220),(25,260),(30,300),(35,330),(40,350)$, find the regression line of sales on advertising.

For the ten points $(1,2),(2,4),(3,3),(4,5),(5,7),(6,8),(7,6),(8,9),(9,10),(10,12)$, find the regression line of $x$ on $y$.