Question

An important application of regression analysis in accounting is in the estimation of cost. By collecting data on volume and cost and using the least squares method to develop an estimated regression equation relating volume and cost, an accountant can estimate the cost associated with a particular manufacturing volume. Consider the following sample of production volumes and total cost data for a manufacturing operation. Total Cost Production Volume (units) 400 4,000 450 5,100 550 5,300 600 5,800 700 6,500 750 7,000 a) Use these data to develop an estimated regression equation that could be used to predict the total cost for a given production volume. (Round your numerical values to two decimal places.) 9 = b) What is the variable cost (in dollars) per unit produced? c) Compute the coefficient of determination. (Round your answer to three decimal places.) What percentage of the variation in total cost can be explained by production volume? (Round your answer to one decimal place.) % d) The company's production schedule shows 650 units must be produced next month. Predict the total cost (in dollars) for this operation. (Round your answer to the nearest cent.)

please help

Answer 1

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	3450.00	33700.00	93750.00	5708333.3	712500.0
mean	575.00	5616.67	SSxx	SSyy	SSxy

a)

Sample size,   n =   6      
here, x̅ = Σx / n=   575.000          
ȳ = Σy/n =   5616.667          
SSxx =    Σ(x-x̅)² =    93750.0000      
SSxy=   Σ(x-x̅)(y-ȳ) =   712500.0      
              
estimated slope , ß1 = SSxy/SSxx =   712500/93750=   7.6000      
intercept,ß0 = y̅-ß1* x̄ =   5616.6667- (7.6 )*575=   1246.6667      
              
Regression line is, Ŷ=   1246.67   + (   7.600   )*x

b) $7.60

c) R² =    (SSxy)²/(SSx.SSy) =    0.949
Approximately 94.9% of variation in observations of variable Y, is explained by variable x

d)

Predicted Y at X=   650   is          
Ŷ=   1246.66667   +   7.60000   *650=   6186.67

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