Liner regression, Liner Regression The calculations for our sample size n = 10 are, Mathematics

Liner regression, Mathematics

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Liner Regression

The calculations for our sample size n = 10 are described below. The linear regression model is y = a + bx

Table:

Distance x miles	Time y mins	xy	x²	y²
3.5	16	56.0	12.25	256
2.4	13	31.0	5.76	169
4.9	19	93.1	24.01	361
4.2	18	75.6	17.64	324
3.0	12	36.0	9.0	144
1.3	11	14.3	1.69	121
1.0	8	8.0	1.0	64
3.0	14	42.0	9.0	196
1.5	9	13.5	2.25	81
4.1	16	65.6	16.81	256
Σx = 28.9	Σy = 136	Σxy = 435.3	Σx^{2 =}99.41	Σy²⁼1972

The Slope b = {(10 * 435.3) - (28.9 * 136)}/ {(10 * 99.41) - (28.9)²} = 2.66

And the intercept a = {136 - (2.66 * 28.9)}/10 = 5.91

Now we insert these values in the linear model describing as

y = 5.91 + 2.66x Or

Delivery time (mins) = 5.91 + 2.66 delivery distance in miles

The slope of the regression line is the estimated number of minutes per mile required for a delivery. The intercept is the estimated time to prepare for the journey and to deliver the goods that is the time required for each journey other than the actual traveling time.

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