the population of a certain country from 1970 through 2010 is shown in the table to the right. use your…

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?\n\nx, number of years after 1969\tpopulation y (millions)\n1 (1970)\t203.8\n11 (1980)\t247.8\n21 (1990)\t252.4\n31 (2000)\t289.2\n41 (2010)\t316.8\n\nthe 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)

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?\n\nx, number of years after 1969\tpopulation y (millions)\n1 (1970)\t203.8\n11 (1980)\t247.8\n21 (1990)\t252.4\n31 (2000)\t289.2\n41 (2010)\t316.8\n\nthe 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)

Answer

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)