# Question: A What is so special about the least squares line that

a. What is so special about the least-squares line that distinguishes it from all other lines?

b. How does the least-squares line “know” that it is predicting Y from X instead of the other way around?

c. It is reasonable to summarize the “most typical” data value as having X as its X value and Y as its Y value. Show that the least-squares line passes through this most typical point.

d. Suppose the standard deviations of X and of Y are held fixed while the correlation decreases from one positive number to a smaller one. What happens to the slope coefficient, b?

b. How does the least-squares line “know” that it is predicting Y from X instead of the other way around?

c. It is reasonable to summarize the “most typical” data value as having X as its X value and Y as its Y value. Show that the least-squares line passes through this most typical point.

d. Suppose the standard deviations of X and of Y are held fixed while the correlation decreases from one positive number to a smaller one. What happens to the slope coefficient, b?

**View Solution:**## Answer to relevant Questions

Define the predicted value and the residual for a given data point. Consider the expense ratio and the total one-year rate of return on the W&R family of mutual funds in Table 11.3.6. a. What percentage of the variation in rate of return is explained by expense ratio? Please provide both the ...Consider the retail price of regular gasoline at selected locations and times shown in Table 11.3.12. a. How strong is the association between prices in 2010 and prices a year earlier? Please give both a number and its ...Now consider also the daily percentage changes in the price of a dollar in Japanese yen from Table 11.3.17, along with the euro. a. Create a scatterplot of the euro’s against the yen’s percentage changes. b. Given that ...In the territory versus sales example (based on the data from Table 11.2.3), the least-squares line to predict sales based on the population of the territory was found to be Expected sales = $1,371,744 +$0:23675045 ...Post your question