Key Terms
Correlation
Cor(x-vector, y-vector)
Bivariate data
Paired data collected on two variables.
Positive correlation
X increases, y increases. Both move together.
Negative correlation
X increases, y decreases. They move opposite.
Excel command
=FORECAST(x_value, y-data range, x-data range)
Standard algebra
Y = mx + b Regression format: y-hat = a + bx
Positive residual
Actual value exceeded the prediction. Negative residual: actual value fell short of the prediction.
Slope (b)
For every one-unit increase in x, y changes by b units, on average.
Example
95% prediction interval for revenue is ($13,270, $15,370) when advertising spend is $80,000. Meaning: there is 95% confi
Intercept (a)
The expected value of y when x = 0.
Beta
Slope of the regression line when stock returns are regressed against a benchmark. Measures systematic risk.
Confidence interval
Estimates the expected MEAN value of y for a given x. Assumes multiple experiments.
Prediction interval
Predict(model, data.frame(x-variable = value), interval = "predict") Output: fit (point estimate), lwr (lower bound), up
Create a vector
Variable <- c(value1, value2, value3)
Linear model
Lm(y-vector ~ x-vector) Note: tilde (~) separates dependent from independent variable. y goes first.