Question

Weight in pounds, X	Miles per Gallon, Y
3779	16
3938	15
2628	26
3616	20
3397	21
2910	22
3733	16
2521	24
3481	19
3881	17
3367	19

a) Find the​ least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable.

y=__x + __

b) Interpret the slope and y-intercept, if appropriate

Answer 1

Ans:

	Weight in pounds, X	Miles per Gallon, Y	xy	x^2	y^2
1	3779	16	60464	14280841	256
2	3938	15	59070	15507844	225
3	2628	26	68328	6906384	676
4	3616	20	72320	13075456	400
5	3397	21	71337	11539609	441
6	2910	22	64020	8468100	484
7	3733	16	59728	13935289	256
8	2521	24	60504	6355441	576
9	3481	19	66139	12117361	361
10	3881	17	65977	15062161	289
11	3367	19	63973	11336689	361
Total	37251	215	711860	128585175	4325

a)

slope,b=(11*711860-37251*215)/(11*128585175-37251^2)=-0.00666

y-intercept,a=(215-(-0.0066607)*37251)/11=42.101

Regression equation:

y'=-0.00666 x+42.101

Slope:

For each unit of increase in weight(in pounds),there will be decrease of 0.00666 miles per gallon.

intercept:

When weight is 0 pounds,Mileage is 42.101