Question

if Sally needs to drive 311 miles home from college and leaves with a full tank how much should she budget to fill up when she gets home ?Assume the regression equation is needed for the prediction. round the answer to nearest cent.x is the top of the chart is miles driveny is the bottom the cost to fill up

Answer 1

First we need to calculate the regression equation

we have the next values

x

292

293

313

305

345

276

337

Sum of X = 2161

Mean X = 308.7143

y

21.85

22.60

24.15

22.90

26.21

21.24

25.02

Then we obtain

Sum of squares (SSX) = 3745.4286=3745-43

Sum of products (SP) = 261.9986=262

the regression equation

$y=mx+b$

for m

$m=\frac{SP}{\text{SSX}}=\frac{262}{3745.43}=0.06995=0.07$

then for b

$b=My-\text{mMx}=23.42-(0.07\cdot308.71)=1.82924=1.83$

the regression equation is

$y=0.07x+1.83$

then if x=311

$y=0.07(311)+1.83=23.60$

She will need 23.60 to fill the tank when she gets home