Question

In: Statistics and Probability

A publisher of books has produced seven comparable Statistical Management books with the following costs. Quantity...

A publisher of books has produced seven comparable Statistical Management books with the following costs.

Quantity

produced

(000)

 1 2 4 5 7 9 13
Manufacturing Cost(000£) 5 5.9 6.5 7.5 8 9.5 10.8

a) (5 pts) Construct the regression line for predicting manufacturing costs from quality produced.

b) (5 pts) Calculate the predicted values and the residuals of this data.

c) (5 pts) Construct a 99% two-sided confidence interval for the intercept.

d) (5 pts) Construct a 99% two-sided confidence interval for the slope.

e) (5 pts) Test for significance of regression by ANOVA and interpret your conclusion.

Solutions

Expert Solution

No x y (x-xbar)^2 (y-ybar)^2 (x-xbar)*(y-ybar)
1 1 5 23.591837 6.76 12.62857143
2 2 5.9 14.877551 2.89 6.557142857
3 4 6.5 3.4489796 1.21 2.042857143
4 5 7.5 0.7346939 0.01 0.085714286
5 7 8 1.3061224 0.16 0.457142857
6 9 9.5 9.877551 3.61 5.971428571
7 13 10.8 51.020408 10.24 22.85714286
sum 41 53.2 104.85714 24.88 50.6
mean 5.857142857 7.6 sxx syy sxy

calculation below using excell

slope = b1 = sxy/sxx = 0.482561308
intercept = b0 = ybar-(slope*xbar) = 4.773569482
SST = SYY = 24.88
SSR = sxy^2/sxx = 24.41760218
SSE = syy-sxy^2/sxx = 0.46239782
r^2 = SSR/SST = 0.981414879
r = sxy/sqrt(sxx*syy) = 0.990663858
error variance s^2 = SSE/(n-2) = 0.092479564
S^2b1 = s^2/sxx = 0.000881958
standard error b1 = se(b1) = sqrt(s^2b1) = 0.029697773
test statistics = b1/se(b1) = 16.24907413
For (1-alpha)% CI value of t = 0.99 = 4.032142984
Lower Confidence bound for slope = estimated slope -t*se(b1) = 0.362815643
Upper Confidence bound for slope = estimated slope +t*se(b1) = 0.602306973
standard error b0 = se(b0) = s*sqrt(1/n+ Xbar^2/Sxx) = 0.208489604
Lower Confidence bound for Intercept = estimated intercept -t*se(b0) = 3.932909588
Lower Confidence bound for Intercept = estimated intercept +t*se(b0) = 5.614229376

a) (5 pts) Construct the regression line for predicting manufacturing costs from quality produced.

slope = b1 = sxy/sxx = 0.482561308 =
intercept = b0 = ybar-(slope*xbar) = 4.773569482 =

y= 4.7736 + 0.4826*x

y=Manufacturing Cost

x=Quantity produced

Regression Model is

Manufacturing Cost =4.7736 + 0.4826*Quantity produced

=======================================================

b)

Observation x y Predicted y Residuals
1 1 5 5.256131 -0.25613
2 2 5.9 5.738692 0.161308
3 4 6.5 6.703815 -0.20381
4 5 7.5 7.186376 0.313624
5 7 8 8.151499 -0.1515
6 9 9.5 9.116621 0.383379
7 13 10.8 11.04687 -0.24687

=======================================================

c) 99% two-sided confidence interval for the intercept.

intercept = b0 = ybar-(slope*xbar) = 4.7736

For (1-alpha)% CI value of t (1-alpha=0.99) = 4.0321

standard error b0 = se(b0) = s*sqrt(1/n+ Xbar^2/Sxx) = 0.208489604
Lower Confidence bound for Intercept = estimated intercept -t*se(b0) = 3.9329
Lower Confidence bound for Intercept = estimated intercept +t*se(b0) = 5.6142

99% two-sided confidence interval for the Intercept=(3.9329 ,5.6142)

=======================================================

d)99% two-sided confidence interval for the slope

slope = b1 = 0.4826

standard error b1 = se(b1) = sqrt(s^2b1) = 0.029697773
For (1-alpha)% CI value of t (1-alpha=0.99) = 4.0321
Lower Confidence bound for slope = estimated slope -t*se(b1) = 0.3628
Upper Confidence bound for slope = estimated slope +t*se(b1) = 0.6023

99% two-sided confidence interval for the slope =(0.3628 , 0.6023)

===============================================

e)

Test for significance of regression by ANOVA and interpret your conclusion.

ANOVA
df SS MS F Significance F
Regression 1 24.41760218 24.4176 264.0324 1.61E-05
Residual 5 0.46239782 0.09248
Total 6 24.88

Null and alternative Hypothesis

H0: Model is not significant

H1:Overall model is significant

test statistics= F0= MS_Regression/MS_Residual =264.0324

p-value = p(F > F0)=0

Decision:P-value is less close to 0 hence we reject H0

Conclusion : Overall Model is significant

ANOVA
df SS MS F Significance F
Regression 1 24.41760218 24.4176 264.0324 1.61E-05
Residual 5 0.46239782 0.09248
Total 6 24.88

================================================================

If you have any doubt please let me know through comment
     Please give positive vote if you find this solution helpful. Thank you

orchestra answered 2 years ago
Next > < Previous

Related Solutions

Suppose that the British economy produces two goods: laptops and books. The quantity produced and the...
Suppose that the British economy produces two goods: laptops and books. The quantity produced and the prices of these items for 2015 and 2016 are shown in the table below: Year Quantities produced Price ($) 2015 Laptops = 60 Books = 1,000 Laptops = 200 Books = ? 2016 Laptops = 80 Books = ? Laptops = 90 Books = 12 Instructions:Round your answer to two decimal places. a. Let’s assume that the base year was 2015, so that real...
Suppose that the British economy produces two goods: laptops and books. The quantity produced and the...
Suppose that the British economy produces two goods: laptops and books. The quantity produced and the prices of these items for 2015 and 2016 are shown in the table below: Year Quantities produced Price ($) 2015 Laptops = 50 Books = 1,000 Laptops = 250 Books = ? 2016 Laptops = 90 Books = ? Laptops = 150 Books = 10 Instructions: Round your answer to two decimal places. a. Let’s assume that the base year was 2015, so that...
You’re a publisher of University Mac Books. A teacher at MSU  has written a new Finance text...
You’re a publisher of University Mac Books. A teacher at MSU  has written a new Finance text book & has asked your firm to prepare & print the text book. She is willing to commit to purchasing 22,000 text books over four years. You are at full production, so you need to purchase new printing equipment at a cost of $3.6Million which will be depreciated on a straight line basis over the life of the project & can be sold for...
The table shows the quantity produced and the total, average, variable, cost, and marginal costs for a firm. Complete the table.
Unit 9— Cost, Revenue, and ProfitThe table shows the quantity produced and the total, average, variable, cost, and marginal costs for a firm. Complete the table.QuantityTotal CostVariable CostFixed CostAverage Total CostAverage Variable CostAverage Fixed CostMarginal Cost00N/AN/AN/AN/A110050502953180130354502052251751025626121174983853359450106855185Graph the total cost, variable cost, and fixed cost curves.Assume the price is $50, draw the total revenue curve and identify the profit maximizing output level and the maximum profitGraph the average total cost, average variable, average fixed, and marginal cost curvesAssume the price is...
A) We are evaluating a project that costs $111518, has a seven-year life, and has no...
A) We are evaluating a project that costs $111518, has a seven-year life, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 4266 units per year. Price per unit is $51, variable cost per unit is $24, and fixed costs are $83124 per year. The tax rate is 39 percent, and we require a 13 percent return on this project. Suppose the projections given for price, quantity,...
A) We are evaluating a project that costs $115571, has a seven-year life, and has no...
A) We are evaluating a project that costs $115571, has a seven-year life, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 4293 units per year. Price per unit is $45, variable cost per unit is $25, and fixed costs are $81427 per year. The tax rate is 35 percent, and we require a 8 percent return on this project. Suppose the projections given for price, quantity,...
A certain monopoly has a marginal cost that depends on the quantity produced. The marginal cost...
A certain monopoly has a marginal cost that depends on the quantity produced. The marginal cost is MC = 4Q The marginal revenue curve is: MR = 40 – 4Q The demand curve is: D = 40 - 2Q Fixed cost of production $10, variable cost is $5 per unit produced. a) Graph the MR, MC and demand curves! b) Which quantity the monopoly will produce at which price? c) Calculate the profit!
Q17    The following data relate to a popular book sold by a publisher: Fixed Costs: Copy Editing...
Q17    The following data relate to a popular book sold by a publisher: Fixed Costs: Copy Editing $ 6,110 Artwork $ 2,250 Typesetting $ 70,853 Variable Costs per copy: Printing and Binding $ 3.17 Bookstore Discounts $ 4.14 Sales Commissions $ 0.59 Author’s Royalties $ 2.44    Each novel copy sells for $ 24 Last month the company sold in copies: 10,771 Production manager suggests to buy an additional machine for $5,250 cost per month and will decrease the variable cost...
The manufacturer of a particular bicycle model has the following costs associated with the management of...
The manufacturer of a particular bicycle model has the following costs associated with the management of this product's inventory. In particular, the company currently maintains an inventory of 1000 units of this bicycle model at the beginning of each year. If X units are demanded each year and X is less than 1000, the excess supply, 1000 − X units, must be stored until next year at a cost of $50 per unit. If X is greater than 1000 units,...
The manufacturer of a particular bicycle model has the following costs associated with the management of...
The manufacturer of a particular bicycle model has the following costs associated with the management of this product's inventory. In particular, the company currently maintains an inventory of 1000 units of this bicycle model at the beginning of each year. If X units are demanded each year and X is less than 1000, the excess supply, 1000 − X units, must be stored until next year at a cost of $50 per unit. If X is greater than 1000 units,...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT