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

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.

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

In an experiment the reaction rate $x$ (mol/s) and temperature $y$ ($^\circ\text{C}$) 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.

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

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 $y$.

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 $y$.

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

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 $y$.

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 $y$.