Final answer:
The correct statements about the regression equation y = 1.8x - 7 are: b) an increase in height by one inch results in an expected weight increase of 1.8 pounds, e) x and y may be strongly correlated (though we cannot be certain without the correlation coefficient), and f) a height of 55 inches predicts a weight of 92 pounds.
Step-by-step explanation:
The equation of the regression line is y = 1.8x - 7, where y represents the weight of the 10-year-old boy in pounds and x represents the height in inches. To determine which statements are correct, we analyze them in relation to the regression equation:
- b. If the height increases by one inch, then the weight is expected to increase by 1.8 pounds. This is correct because 1.8 is the slope of the regression line, indicating the change in weight for each one-inch increase in height.
- e. x and y are strongly correlated. While the regression equation itself doesn't provide the correlation coefficient, typically, a regression line is created when a strong correlation exists between the variables. However, without the correlation coefficient value, this cannot be confirmed.
- f. A 10-year-old with a height of 55 inches is expected to have a weight of 92 pounds. Using the equation y = 1.8(55) - 7, we find that y = 99 - 7, which equals 92 pounds. This is a correct application of the regression line.
The other statements are incorrect because:
- a. If we put 65 pounds for y, solving for x does not give us 40 inches.
- c. A height of zero would predict a weight of -7 pounds, which doesn't make sense physically.
- d. This statement misinterprets the slope of the line; the increase in height does not directly cause the increase in weight, and the units are not interchangeable.