Assessing a trend line

Statistical Techniques in Tableau

Maarten Van den Broeck

Content Developer at DataCamp

Linear and logarithmic models

Linear Linear model of species richness vs. distance, with a trend line.

Logarithmic Linear model of species richness vs. distance, with a logarithmic line.

Linear model

Linear model of species richness vs. distance, with a linear trend line.

$y=a*x+b$
Regression: quantify how $x$ causes $y$ to change
$a$ = slope, $b$ = intercept
$richness = a * distance + b$
$richness = 0.0038 * distance + 13.4$

Residuals and $R^2$ of linear model

Linear model of species richness vs. distance, with a linear line.

Goal is to minimize distance between observation and trend line
The distance is called a residual
Coefficient of determination $R^2$
For linear model, $R^2$ = correlation coefficient squared
Between 0 (worst) and 1 (best)
$R^2 = 0.33$
Explains $n\%$ of the variation

$R^2$ of logarithmic model

Linear model of species richness vs. distance, with a logarithmic line.

$R^2 = 0.59$

Residual standard error (RSE)

Average difference between observed values and trend line
Linear model: RSE = 3.69
Confidence interval is wider at low and high distances

Same unit as unit on y axis
Logarithmic model: RSE = 2.91
Confidence interval is only wider at very high distances

p-value

Linear model

p-value = 0.001
Chance of $\frac{1}{1000}$ there is no correlation
p-value < 0.05: model is statistically significant, fits data well

Logarithmic model

p-value = 0.0001
Chance of $\frac{1}{10000}$ there is no correlation
The lower the p-value, the better, but p-value isn't everything!

Let's practice!

Statistical Techniques in Tableau

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