Chapter 12.3, Problem 23AYU

Influential Observations Zillow.com is a site that can be used to assess the value of homes in your neighborhood. The organization provides a list of homes for sale as well as a Zestimate, which is the price Zillow believes the home will sell for. The data on the next page represent the Zestimate and sale price (in thousands of dollars) of a random sample of recently sold homes in Charleston. South Carolina.

Zestimate	Sale Price
362	370
309	315
365.5	371.9
215	218
184	186.5
252.5	260
247.5	250.8
244	251

Source: zillow.com

1. a. Draw a scatter diagram of the data, treating the Zestimate as the explanatory variable and sale price as the response variable.
2. b. Determine the least-squares regression line. Test whether there is a relation between the Zestimate and sale price at the α = 0.05 level of significance.
3. c. An observation is said to be influential if the inclusion of the observation significantly changes the value of the slope and/or intercept of the least-squares regression line. A home with a Zestimate of $370,000 recently sold for $150,000. Determine the least-squares regression line with this home included. Test whether there is a relation between the Zestimate and sale price at the α = 0.05 level of significance. Do you think this observation is influential?