Annual high temperatures in a certain location have been tracked for several years.

Question

Annual high temperatures in a certain location have been tracked for several years. Let X represent the year and Y the high temperature. Assume that temperature is independent each year.

Based on the data shown below, calculate the regression line (each value to two decimal places). First the slope and then the y-intercept.

xy
4	11.28
5	11.25
6	12.52
7	15.19
8	16.96
9	16.33
10	19.9
11	18.07
12	22.74
13	24.01
14	24.78
15	25.15
16	26.42
17	26.19
18	27.06

Answer 1

Hi Emma,

Plug those lists into a TI-80s series calculator. Designate x, the year, as L1 and y, the temperature, as L2. Go to STAT-EDIT-and enter your data. Then, go to STAT-CALC-LinReg ax + b, enter L1,L2. This will give you the equation of the regression line in the form y = ax + b.

Equation: y^ = 1.25x + 6.06

Slope: 1.25

Intercept: 6.06

Note that this same procedure also gives you the correlation coefficient r, and the coefficient of determination, r². In this case, they are 0.98 and 0.96 respectively. I noticed you posted other problems asking for these values, so do the same computations in your calculator for those. I hope this helps.