Final answer:
The equation of the regression line for the relationship between building stories and height can be found using the least-squares method, resulting in an equation of the form ý = a + bx, where 'a' is the y-intercept, and 'b' is the slope. The slope indicates the change in height per story, and the y-intercept is the estimated height at zero stories. Precise calculations require statistical tools and are necessary to make predictions for specific values of x (number of stories).
Step-by-step explanation:
To find the equation of the regression line for the heights and number of stories of buildings, one must perform a statistical analysis on the given data. With the number of stories as the independent variable (x) and the height as the dependent variable (y), a scatter plot is created to visualize the relationship between these two variables. After plotting the data, we use a statistical tool (like a calculator or software) to calculate the least-squares regression line. The general form of the equation is ý = a + bx, where ý is the predicted height (y), 'a' is the y-intercept, and 'b' is the slope of the line.
The slope ('b') represents the average change in height for each additional story, while the y-intercept ('a') represents the estimated height when the number of stories is zero. To predict the height for a building with a certain number of stories, we substitute the value of 'x' (the number of stories) into the regression equation.
Without the actual calculations done, we cannot provide the exact regression equation or the predictions for specific numbers of stories. However, the process described above outlines the steps necessary to find and use the regression equation to make predictions.