1: (20 marks) 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 Dependent 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: Write Equations 2 and 4 in the form y = a + bx. (4 marks) If actual sales are $1,500,000 in 2013, what would be the forecasted sales for Lockit in 2014 (4 marks) Explain the meaning and significance of the coefficient of correlation. (4 marks) Why might Larry Husky prefer Equation 3 to Equation 2? (4marks) Explain the advantages and disadvantages of using Equation 4 to forecast annual sales. (4 marks)