Question

find the equation for the least squares regression line of the data described below. a pharmaceutical company is testing a new headache medication. researchers at the company conducted an observational study using volunteer participants. all participants were given a supply of tablets of the new medication. the participants then recorded how many headaches they had had for a week, x, and how many tablets they had taken, y. headaches | tablets 3 | 1 4 | 3 5 | 10 6 | 2 10 | 5 round your answers to the nearest thousandth. y = x +

Explanation:

Step1: Calculate sums for regression

$n=5$, $\sum x = 3+4+5+6+10 = 28$, $\sum y =1+3+10+2+5=21$, $\sum xy=(3*1)+(4*3)+(5*10)+(6*2)+(10*5)=3+12+50+12+50=127$, $\sum x^2 = 3^2+4^2+5^2+6^2+10^2=9+16+25+36+100=186$

Step2: Compute slope $m$

$$ m = \frac{n\sum xy - \sum x \sum y}{n\sum x^2 - (\sum x)^2} = \frac{(5*127) - (28*21)}{(5*186) - 28^2} = \frac{635 - 588}{930 - 784} = \frac{47}{146} \approx 0.322 $$

Step3: Compute intercept $b$

$$ b = \frac{\sum y - m\sum x}{n} = \frac{21 - 0.322*28}{5} = \frac{21 - 9.016}{5} = \frac{11.984}{5} \approx 2.397 $$

Answer:

$y = 0.322x + 2.397$