Final answer:
The equation for the best-fit regression line is ŷ = -173.51 + 4.83x, where ŷ is the estimated value, x is the independent variable, -173.51 is the y-intercept, and 4.83 is the slope. The r-squared and r values indicate the predictability and strength of the relationship between variables.
Step-by-step explanation:
To write the equation for the best-fit regression line, you can use a series of steps including making a scatter plot of your data, using a calculator’s regression function to calculate the least-squares regression line, and plotting this line on your scatter plot. The equation for the best-fit line has the form ŷ = mx + b, where ŷ is the estimated value of the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept. In the example provided, the regression equation is ŷ = -173.51 + 4.83x. The r-squared value, r² = .43969, indicates the proportion of variance in the dependent variable that's predictable from the independent variable, and r = .663 gives the strength and direction of the correlation between the variables.
To predict the height of someone based on their pinky length using your line of best fit, you would substitute the pinky length into your regression equation. The value of the slope represents the change in the predicted y value for each additional unit increase in x, while the y-intercept represents the predicted y value when x is zero. If your r value is close to zero, it means there is little to no linear relationship between the variables.