Answer :
Given data where the -value represents the area to be painted in square feet and the -value represents amount of paint in gallons, the regression curve is likely a) linear.
To determine whether the regression curve is likely linear or non-linear, consider the relationship between the area to be painted (in square feet) and the amount of paint (in gallons).
Linear Relationship:
- If the amount of paint required increases consistently with the area to be painted (e.g., a constant amount of paint is needed per additional unit of area), the relationship is likely linear.
- This means the data points would fit well to a straight line, and the equation of the regression line would be of the form y = mx + b, where m is the slope and b is the y-intercept.
Non-linear Relationship:
- If the amount of paint required increases at a rate that is not constant relative to the area (e.g., the paint needed per unit area changes as the area increases), the relationship is likely non-linear.
- This could mean the regression curve is a curve such as a polynomial or exponential function, fitting the data in a more complex manner than a straight line.
