The owner of a moving company typically has his most experie

The owner of a moving company typically has his most experienced manager predict the total number of labor hours that will be required to complete an upcoming move. In a effort to provide a more accurate method, the owner has decided to use the number of cubic feet moved as the independent variable and has collected data for 20 moves in which the travel time was an insignificant portion of the hours worked. Using the least-squares method on this data finds that b_0 = 0.4283 and b_1 = 0.0534, and that the predicted labor hours for moving 400 cubic feet is 21.79 hours. Complete parts (a) through (c) below.

Solution

x: Cubic feet as independent variable

y: Labor Hours as dependent variable

we fit the regression for the given set of data using least square and level of significance is 95 % using data analysis tool in Excel. Result is as follows ;

The regression equations is

Labour Hours = 2.364 + 0.051 * Cubic Feet ..............................................(i)

now we calculate the labour hour when cubic feet is 400.

from equation (i)

labour hour = 2.364 + 0.051 * 400 = 22.764

Regression Statistics
Multiple R	0.9658
R Square	0.9328
Adjusted R Square	0.9291
Standard Error	2.7513
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1891.98	1891.98	249.94	0.00
Residual	18	136.25	7.57
Total	19	2028.24
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	2.364	1.941	1.218	0.239	-1.714	6.443
Cubic feet	0.051	0.003	15.810	0.000	0.044	0.058