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Problem 53

The median price of existing single-family homes has increased consistently during the past few years. However, the data in Table 1.4 show that there have been differences in various parts of the country.

(a) Find the linear regression equation for home cost in the South.
(b) What does the slope of the regression line represent?
(c) Find the linear regression equation for home cost in the West.
(d) Where is the median price increasing more rapidly, in the South or the West?

a) $y=5980 x-1.18098 \times 10^{7}$
b) $\$ 5980,$the average annual increase of the home cost in the South c)$y=21650 x-4.3105 \times 10^{7}\$
d) In the West.

## Discussion

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## Video Transcript

we have been given the table that represents the medium price of existing single family homes in both the South and in the West. In part A were asked to find the linear regression equation for home cost in the self. To do this, we need to enter our data into a graphing calculator north of find a linear regression model. Upon entering the data, you will find that the model that represents the home cost in the South is by the linear equation. Why equals 5980 x minus 11 million 100 9000 820. And this equation is represents the rainy aggression equation for the home cost in the self. Next, in Part B were asked what the slope of this regression equation represents. Well, the slope is 5980 and remember, Slope represents the rate of change in the particular set of data, while our data is representing the increasing dollars per year. So what our soap represents in this case is 5980 represents the average increase in the home cost in the South. Next were asked to find in part in sea of linear regression equation for home costs in the West. So similarly, to part A, we're going to use our graphing calculator toe into the data. But now for the home cost for the West. Upon doing so, what we find is that the linear regression equation is why equals 21,000 650 x, minus 43 million 105,000 30. So again, the linear regression equations so that represents the home cost in the West is why equals 21,650 x, minus 43,105,030. Lastly, in Part D were asked, where is the medium price increasing more rapidly in the south or the West? Well, the soap of our lines is is going to give us this piece of information because the slope of the line in part A is only 5980 and the soap in part see which represents the rest is 21,650. Because the slope in part C is higher than in part a. What we find is that the West is where the median price is increasing at a more rapid rate