Models

We develop a linear regression model for each plot using the lm() function built into R. We then find Pearson’s correlation coefficient \((R)\) to measure the strength of the relationship between our variables of interest.

\[y_i = \beta_0 + \beta_1X_i + \epsilon_i\] with \(y = dependent\:variable\), \(\beta_0 = intercept\), \(\beta_1 = regression\:coefficient\), \(X = independent\:variable\), and \(\epsilon = error\)

	Education Ranking
Predictors	Estimates	CI	p	Estimates	CI	p
(Intercept)	128.67	96.35 – 161.00	<0.001	156.84	116.79 – 196.88	<0.001
score	-0.21	-0.28 – -0.14	<0.001
iq				-1.37	-1.81 – -0.94	<0.001
Observations	56			56
R2 / R2 adjusted	0.408 / 0.397			0.426 / 0.415

	IQ
Predictors	Estimates	CI	p
(Intercept)	25.03	17.06 – 33.00	<0.001
score	0.15	0.13 – 0.16	<0.001
Observations	56
R2 / R2 adjusted	0.841 / 0.838