Sample Problem

 Year The number of jalapenos on Mars (in thousands) 1970 40 1971 40 1972 42 1973 47 1974 54 1975 57 1976 63 1977 65 1978 68 1979 77 1980 81 1981 82 1982 88 1983 92 1984 95 1985 99 1986 100 1987 110 1988 114 1989 121 1990 130

Why is it so hot on Mars? Since they discovered the fourth planet from the Sun, scientists have been in the midst of heated debates and deep speculation. Last year, a scientist named John Kosher Shaw from Dirty Potato Chipville, Louisiana noticed an uncanny growth of jalapeno pepper populations on the planet. Could this be the reason why Mars is so hot? Above is a table of the number of jalapeno peppers on Mars (in the thousands) over a 20 year period (1970-1990).

Let t=0 represent the year 1970 and let y represent the number of jalapeno peppers (in thousands) on Mars.

Your task is, using the linear regression feature on your graphing calculator, find a least squares regression line to predict, based on this trend, what the jalapeno pepper populations were after 1990.

y=x+ (round your answers to the nearest tenth)

Solution After plugging in all the values into the graphing calculator (remember to replace the actual years with the year numbers, starting with 1970= Year 0, 1971=Year 1…etc.), your graph should look something like this. Using the linear regression function on the graphing calculator, you should be able to get the slope and y-intercept value of the “best-fit” line, or least squares regression line.

LinReg

y=ax+b

a=4.397402597

b=35.31168831

y=4.4x+35.3