The Lockit Company manufactures door knobs for residential homes and apartments.

Question

The Lockit Company manufactures door knobs for residential homes and apartments. Lockit is considering the use of simple and multiple linear regression analysis to forecast annual sales because previous forecasts have been inaccurate. The sales forecast will be used to initiate the budgeting process and to identify better the underlying process that generates sales.

Larry Husky, the controller of Lockit, has considered many possible independent variables and equations to predict sales and has narrowed his choices to four equations. Husky used annual observations from twenty prior years to estimate each of the four equations.

Following is a definition of the variables used in the four equations and a statistical summary of these equations:

St = Forecasted sales (in dollars) for Lockit in time period t

St-1 = Actual sales (in dollars) for Lockit in time period t 1

Gt = Forecasted United States gross national product in time period t

G t-1 = Actual United States gross national product in time period t 1

N t-1 = Lockit's net income in time period t – 1

Statistical Summary of Four Equations

Coefficients

Independent Standard Coefficient

Dependent Independent Variable Variable Error of of

Equation Variable Variable(s) (Intercept) (Rate) the Estimate Correlation tValue

1 St St-1 +$ 500,000 +$ 1.10 $500,000 +.97 5.50

2 St Gt +$1,000,000 +$ .00001 $510,000 +.95 10.00

3 St Gt-1 +$ 900,000 +$.000012 $520,000 +.90 5.00

St +$ 600,000 $490,000 +.98

Nt-1 +$ 10.00 4.00

4 Gt +$.000002 1.50

Gt-1 +$.000003 3.00

Required

a Write Equations 2 and 4 in the form y = a + bx.

b If actual sales are $1,500,000 in 2017, what would be the forecasted sales for Lockit in 2018?

c Explain the meaning and significance of the coefficient of correlation.

d Why might Larry Husky prefer Equation 3 to Equation 2?

e Explain the advantages and disadvantages of using Equation 4 to forecast annual sales.

Explanation / Answer

Solution:

1.         Equation 2: St = $1,000,000 + $0.00001Gt

            Equation 4: St = $600,000 + $10Nt–1 + $0.000002Gt + $0.000003Gt–1

2.         To forecast 2010 sales based on 2009 sales, Equation 1 must be used:

            St = $500,000 + $1.10St–1

            S2010     = $500,000 + $1.10($1,500,000)

                        = $2,150,000

3.         Equation 2 requires a forecast of gross domestic product. Equation 3 uses the actual gross domestic product for the past year and, therefore, is observable.

4.         Advantages: Using the highest R2, the lowest standard error, and the equation involves three variables. A more accurate forecast should be the outcome.

            Disadvantages: More complexity in computing the formula.

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