Question

Area	Price
2675	179,000
1170	125,900
1486	136,750
2510	172,500
2444	169,900
2980	187,00

Using area as the independent variable, find a model for the data. Round to the nearest hundredth.

Answer 1

A scatterplot of the given data is attached. The data resembles the graph of a linear function.

Let the linear function be y = mx+c, where x is the area, y is the price in dollars and m,c are arbitrary real numbers.

When x =2675, y = 179900 and when x =2980, y = 187000 so that m = (187000-179900)/(2980-2675) = 7100/5655 = 1420/1131 = 1.26 ( on rounding off to the nearest hundredth).

Thus, y = 1.26x+c.

Now, on substituting x = 1170 and y = 125900 in this equation, we get 125900 = 1.26*1170+c or, c = 125900- 1474.20 = 124425.80. Hence, the required linear model is y = 1.26x +124425.80.