The least squares regression line for a set of data is calculated to be y = 24.8 + 3.41x. (a) One of the points in the data set is (4, 37). Calculate the predicted value. (b) For the point in part (a), calculate the residual.
Linear Regression: Understand the concept of linear regression, which is a statistical method used to model the relationship between a dependent variable (usually denoted as "y") and one or more independent variables (usually denoted as "x"). In simple linear regression, there's only one independent variable.
Least Squares Method: Be familiar with the least squares method, which is used to find the best-fitting line (regression line) through a set of data points by minimizing the sum of the squared differences between the observed values and the predicted values.
Regression Equation: Understand the structure of the regression equation, which typically takes the form: ŷ = a + bx, where ŷ represents the predicted (estimated) value of the dependent variable, a is the intercept, b is the slope, and x is the independent variable.
Predicted Value (ŷ): Know how to calculate the predicted value (ŷ) for a given data point by substituting the independent variable value (x) into the regression equation.
Residuals: Be aware of what residuals are in the context of linear regression. Residuals represent the differences between the observed values (actual data points) and the predicted values from the regression line. You calculate residuals as Actual (y) - Predicted (ŷ).
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