How many data sets are required to implement linear regression?

• A. One
• B. Three
• C. Four
• D. Two

Answer: (D)

In simple linear regression you’re trying to estimate two quantities: the intercept and the slope of the line that best fits the data. Because there are two unknown parameters, you need at least two independent observations to determine them. With two data points, you can draw a unique line that passes through both, giving a definite estimate for both parameters (though with only two points, the estimate isn’t robust to variability). As you add more data points, the estimation becomes more reliable by averaging out noise. In general, for a model with p predictors, you’d need at least p+1 observations to identify all parameters. So the minimum number of data points to implement simple linear regression is two.