Final answer:
To calculate the line of best fit, data points are entered into a calculator, a scatter plot is created, and the calculator's regression function is used to estimate the regression line. Predictions are made by substituting x-values into the regression equation, and residuals are calculated by subtracting the predicted y-value from the actual y-value.
Step-by-step explanation:
To calculate the line of best fit using a calculator, first enter the given data points into the calculator. If you are using a graphing calculator like the TI-83 or TI-84, you would typically follow these steps:
- Enter the data into the 'STAT' 'Edit' menu as two lists; one for the x-values and one for the y-values.
- Next, create a scatter plot by going to 'STAT PLOT' and enabling Plot1.
- Select the scatter plot icon and choose the lists you used for the x and y data.
- Press 'GRAPH' to view the scatter plot.
- To find the regression line, go back to 'STAT', over to 'CALC', and select 'LinReg(ax+b)'.
- After the calculation, the calculator will give you the slope (a) and y-intercept (b), rounding to four decimal places, which form the least-squares regression line.
To predict a value, input the x-value into the equation. For instance, if the equation is y = ax + b and x is 5 hours, you would calculate y by substituting 5 into the equation for x.
Finally, to find the residual for a person who slept 5 hours, subtract the actual y-value (if given) from the predicted y-value from the regression equation. The formula for the residual is: residual = actual y - predicted y.