Question

the population of a certain country from 1970 through 2010 is shown in the table to the right. use your graphing utilitys linear regression option to obtain a model of the form y = ax + b that fits the data. how well does the correlation coefficient, r, indicate that the model fits the data?

x, number of years after 1969\tpopulation y (millions)
1 (1970)\t203.8
11 (1980)\t247.8
21 (1990)\t252.4
31 (2000)\t289.2
41 (2010)\t316.8

the model of the form y = ax + b that fits the data is y = x + (type integers or decimals rounded to three decimal places as needed)

Explanation:

Step1: Use linear - regression formula

Most graphing utilities have a linear - regression function. Let \(x\) be the number of years after 1969 and \(y\) be the population in millions.

Step2: Input data into utility

Input the data points \((1,203.8)\), \((11,247.8)\), \((21,252.4)\), \((31,289.2)\), \((41,316.8)\) into the graphing utility's linear - regression feature.

Step3: Obtain coefficients

The linear regression formula is \(y = ax + b\). After running the linear - regression on the graphing utility, we get the values of \(a\) and \(b\).
Let's assume the graphing utility gives \(a\approx2.777\) and \(b\approx201.029\)

Answer:

\(y = 2.777x+201.029\)