CAN YOU PLEASE MAKE SURE TO ANSWER THE CALCULATED QUESTIONS

Multiple Regression

In the McCourt Company example,

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percent of the variability in materials handling cost was explained by changes in the number of moves. As a result, McCourt may want to search for additional explanatory variables. For example, the weight of the items moved might be useful$$particularly if forklifts and other heavy machinery are needed for moving parts and products from one location to another.

In the case of two explanatory variables, the linear equation is expanded to include the additional variable:

Y $=$ F $+$ V$1$X$1+$ V$2$X$2$

where

X$1=$ Number of moves

X$2=$ Number of pounds moved

With three variables $($Y$,$ X$1,$ X$2),$ a minimum of three points is needed to compute the parameters F$,$ V$1,$ and V$2.$ Seeing the points becomes difficult because they must be plotted in three dimensions. Using the scatterplot method or the high$-$low method is not practical.

However, the extension of the method of least squares is straightforward. It is relatively simple to develop a set of equations that provides values for F$,$ V$1,$ and V$2$ that yields the best$-$fitting equation. Whenever least squares is used to fit an equation involving two or more independent variables, the method is called multiple regression. The computations required for multiple regressions are far more complex than in simple $($one independent variable$)$ regression and any practical application of multiple regression requires use of regression software. The reliability measures are basically the same for multiple regressions as they were for a regression involving a single variable.

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Applying the Concepts

The staff of controller of McCourt Company added the variable "pounds moved" to the ten$-$month data set:

Month

Materials Handling Cost

Number of Moves

Pounds Moved

January

$$5,600$

$475$

$12,000$

February

$3,090$

$125$

$15,000$

March

$2,780$

$175$

$7,800$

April

$8,000$

$600$

$29,000$

May

$1,990$

$200$

$600$

June

$5,300$

$300$

$23,000$

July

$4,300$

$250$

$17,000$

August

$6,300$

$400$

$25,000$

September

$2,000$

$100$

$6,000$

October

$6,240$

$425$

$22,400$

Required:

$1.$ Using the data on material handling, use regression software such as Microsoft Excel to complete the missing data in the table below $($round regression parameters to the nearest cent and other answers to three decimal places$)$:

McCourt Company

SUMMARY OUTPUT

Regression Statistics

Multiple R

$0\mathrm{.}999$

R Square

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Adjusted R Square

fill in the blank $7$e$954$eff$8$ff$5$fa$6\_2$

Standard Error

$119\mathrm{.}600$

Observations

$10$

ANOVA

df

SS

MS

F

Significance F

Regression

$2$

$37,768,070\mathrm{.}16$

$18,884,035$

$1,320\mathrm{.}168$

$9\mathrm{.}50629$E$-10$

Residual

$7$

$100,129\mathrm{.}84$

$14,304\mathrm{.}26$

Total

$9$

$37,868,200\mathrm{.}00$

Coefficients

Standard Error

t Stat

P$-$value

Intercept

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$86\mathrm{.}068$

$6\mathrm{.}863$

$0\mathrm{.}000239$

X Variable $1$

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$0\mathrm{.}340$

$0\mathrm{.}340$

$9\mathrm{.}81$E$-08$

X Variable $2$

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$0\mathrm{.}006$

$17\mathrm{.}446$

$5$E$-07$

$2.$ Using the cost equation from Requirement $1,$ calculate the total expected material handling cost for November if $350$ moves are expected and $17,000$ pounds of material will be moved $($round final answer to the nearest dollar$).$

Expected material handling cost: $

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$3.$ For the coming year, McCourt expects $3,940$ moves involving a total of $204,000$ pounds. Calculate the following:

Total expected fixed costs $($round to the nearest dollar$)$: $

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Total material handling cost $($add each component in the equation and then round to the nearest dollar$)$: $

fill in the blank $7$e$954$eff$8$ff$5$fa$6\_8$