In linear regression using the least squares method, what is the expected shape or equation of the calibration plot relating the dependent variable to the independent variable?

• A. A horizontal line described by the equation $y=a$
• B. A parabola described by the equation $y=a+b{x}^2$
• C. A straight line described by the equation $y=a+bx$
• D. An exponential curve described by the equation $y=a{b}^x$

Answer: (C)

Verified step by step guidance

1. Understand that in linear regression using the least squares method, we model the relationship between the dependent variable \(y\) and the independent variable \(x\) with a linear equation.
2. Recall that the general form of a linear equation is \(y = a + b x\), where \(a\) is the intercept (the value of \(y\) when \(x=0\)) and \(b\) is the slope (the rate of change of \(y\) with respect to \(x\)).
3. The least squares method finds the values of \(a\) and \(b\) that minimize the sum of the squared differences between the observed values and the values predicted by the linear model.
4. Because the model is linear, the calibration plot (a graph of predicted \(y\) versus \(x\)) will be a straight line, not a curve or parabola.
5. Therefore, the expected shape or equation of the calibration plot is a straight line described by the equation \(y = a + b x\).