Final answer:
The question is about conducting a polynomial regression analysis to fit a parabola through a given set of points, then finding the equation of that parabola using calculator functions. The resulting equation of the parabola is displayed on a scatter plot to visualize the fit.
Step-by-step explanation:
The question involves creating a parabolic regression model using a set of data points. The process begins with entering the data into a calculator and creating a scatter plot. Following this, the calculator's regression function is used to find the best-fit parabola, which is also referred to as the least-squares regression parabola - a concept very similar to the least-squares regression line, but adapted for instances where a parabolic (second degree polynomial) pattern is present in the data.
The equation of the parabola typically takes the form ŷ = ax² + bx + c, where a, b, and c are calculated by the regression function based on the input data to minimize the sum of squared residuals. This parabolic equation is then added to the scatter plot from Part A to visually confirm the fit of the curve to the data points.
If the task was instead to find a linear best-fit line (which seems to be implied by parts of the question), one would calculate and use an equation of the form ŷ = mx + b, where m is the slope and b is the y-intercept. In both cases, an important step is to analyze the fit of the model by looking at the correlation coefficient (for linear regression) or other indicators of fit for polynomial regression, and deciding if the model is appropriate for the data in question.