Final answer:
The key question for prediction / linear regression modeling concerns how to use a regression equation, like Ŷ = 101.32 + 2.48x, to predict future values based on the linear relationship between variables as indicated by the slope and y-intercept of the regression line.
Step-by-step explanation:
The key question for the concept of prediction / linear regression modeling is how to use a regression equation to make predictions about future outcomes based on the relationship between independent and dependent variables. For instance, given the equation Ŷ = 101.32 + 2.48x, where Ŷ represents the predicted sales in thousands of dollars and x is the day within a 90-day period, you can predict future sales on specific days.
To predict sales on day 60 using the given model, you would substitute 60 for x: Ŷ = 101.32 + 2.48(60). To predict sales on day 90, substitute 90 for x in the equation: Ŷ = 101.32 + 2.48(90).
The regression line's slope indicates the predicted increase in the dependent variable for each one-unit increase in the independent variable. The y-intercept represents the predicted value of the dependent variable when the independent variable is zero. The strength of the linear relationship is measured by the correlation coefficient. If there is a significant correlation and a linear relationship between the variables, then we can use the regression line for prediction.