Final answer:
The y-intercept of the equation y = 1.12 + 0.48x is 1.12, meaning when the mg per day of drug is 0, the model predicts a weight change of 1.12 lbs per month. The slope of the equation is 0.48, indicating the change in weight per one-unit increase in drug dosage. The coefficient of determination, r², calculated from a correlation coefficient of -0.56 for body weight and fuel efficiency, is 0.3136, explaining 31.36% of the variability.
Step-by-step explanation:
The y-intercept of a linear equation y = mx + b is the value of y when x is zero. In the given line of best fit y = 1.12 + 0.48x, the y-intercept is 1.12. This implies that when the mg per day of drug is at 0 mg per day, the model predicts a weight change value of 1.12 lbs per month. The value of the slope in this equation is 0.48, which indicates the change in weight for each one-unit increase in the mg per day of the drug.
The coefficient of determination, denoted as r², can be calculated from the correlation coefficient r, which is -0.56 in the given data of body weight and fuel efficiency. The coefficient of determination is then r² = (-0.56)² = 0.3136. This means that approximately 31.36% of the variability in fuel efficiency can be explained by the variability in body weight in the sample of cars.
For the regression equation predicting weight from height in a set of data, you would normally insert the respective coefficients into the formula y = mx + b. If the average height (x) is 68 inches and the slope and y-intercept were known, you would calculate the predicted weight by substituting these values into the equation. Without the specific coefficients given for this scenario, we cannot calculate the predicted weight.