Question Assignment 1
Suppose that you work for a firm that operates stores throughout a number of markets, and you need to perceive the revenues earned by particular retailer areas. To that finish, you acquire completely different items of details about every retailer, and run the next regression:
case:
(i) “Income” is the income (per worker) per week for every retailer in 1000’s of dollars
(ii) “Dimension of Retailer” is the world of the shop’s floorplan (in sq. metres).
(iii) “Distance to Nearest Main Highway” is the space (in tons of of metres) to the closest Four-lane (or bigger) highway resulting in the shop.
(iv) “Market Dimension” is the variety of folks, in 1000’s, who reside out there served by every retailer.
The regression outcomes from the info you’ve acquired are displayed under:
Coefficient Commonplace Error of Coefficient
Intercept Four 1
Dimension of Retailer zero.1 zero.02
Distance to Nearest Main Highway –1 zero.25
Market Dimension zero.5 zero.1
The questions associated to those outcomes are displayed on the next web page.
(a) What’s the correct, technical interpretation of the coefficient on “Dimension of Retailer” within the a number of regression? (5 marks)
(b) On this a number of regression setting, how would you check the speculation that the impact of “Dimension of Retailer” on revenues was zero on the 5% stage of significance for all markets during which your organization operates? (5 marks)
(c) Once more, on this a number of regression setting, check (on the 5% stage of significance) the speculation that the variable “Distance to Nearest Main Highway” no impact on a retailer’s revenues.
(5 marks)
(d) Now suppose that you purchase one different piece of knowledge: the weekly promoting finances (in 1000’s of dollars) for every specific retailer. You characterize this info with the variable “Promoting Price range”, and your regression is now specified as:
Utilizing this new regression, you acquire the next outcomes:
Coefficient Commonplace Error of Coefficient
Intercept Four 1
Dimension of Retailer zero.01 zero.02
Distance to Nearest Main Highway –1 zero.25
Market Dimension zero.5 zero.1
Promoting Price range 2 zero.Four
On this case, check the speculation that the impact of “Dimension of Retailer” on revenues was zero on the 5% stage of significance for all markets during which your organization operates? (5 marks)
(e) Clarify why the coefficient worth on “Dimension of Retailer” and the speculation check on this coefficient is completely different partially (d) than partially (a) and (b). (10 marks)
Question Assignment 2
You’ve been contracted by a pc producer to check the value of laptop computer computer systems out there. You’re requested to research the determinants of those costs, and so you acquire information on the traits of varied laptops bought by completely different corporations, and use a regression to discover this concern:
On this case:
(v) “Value” is the value of the laptop computer (in dollars)
(vi) “Dimension of display screen” is the world, in sq. centimetres, of the laptop computer’s display screen.
(vii) “Processor Pace” is the pc’s processing pace in GHz. (viii) “RAM” is pc’s reminiscence in GB.
The regression outcomes from the info analyzed by the inner analysis workforce are displayed under:
Coefficient Commonplace Error of the Coefficient
Intercept 500 100
Dimension of display screen –5 2
Processor Pace 200 50
RAM 100 10
Commonplace Error of the Regression = 150
(a) Present a definition of the coefficient on “Processor Pace”, and utilizing the 5% stage of significance, check the speculation that this variable has an impact on the value of the laptop computer. (10 marks)
(b) Suppose that a new laptop computer has been made by this firm that has: (i) a display screen whose space is 120 sq. centimetres, (ii) a processor pace of Four GHz, and (iii) eight GB of RAM. If the corporate believed that a laptop computer like this might have a value of $1000, reply to this assertion by utilizing the knowledge from the regression in addition to formal speculation testing strategies. (10 marks)
(Please see the next web page for the following a part of this Question Assignment)
(c) Now suppose that you do some extra Assessment of the value of laptops by including some info to the regression utilized in components (a) and (b). Particularly, you estimate:
On this case, “Weight” is the burden of the laptop computer (in grams). The outcomes from this regression are displayed under:
Coefficient Commonplace Error of the Coefficient
Intercept 500 100
Dimension of display screen –1 2
Processor Pace 200 50
RAM 100 10
Weight –2 zero.5
Commonplace Error of the Regression = 100
On this case, the coefficient on “Dimension of Display screen” modified on this regression in comparison with the regression partially (a). How can you clarify this coefficient’s change, whereas incorporating the correlation between “Dimension of Display screen” and “Weight” into your reply? (10 marks)
(d) Suppose that the corporate intends to fabricate the identical laptop computer laid out in half (b), however has a particular weight in thoughts. Particularly, the laptop computer it should make has: (i) a display screen whose space is 120 sq. centimetres, (ii) a processor pace of Four GHz, (iii) eight GB of RAM, and (iv) a weight of 400g. If, once more, the corporate believed that a laptop computer like this might have a value of $1000, reply to this assertion by utilizing the knowledge from the regression in addition to formal speculation testing strategies. (10 marks)
Question Assignment three
(a) You work for a giant firm that needs to match the efficiency of two gross sales groups
(we’ll name them “Staff A” and “Staff B”) working on the firm. To formalize this comparability, you collect a pattern of information on the weekly income created by every workforce. You then use this information to estimate the next regression:
On this case, “Income” represents the weekly income (in dollars) generated by the gross sales workforce, and “Staff A” is a dummy variable equal to 1 if the income is created by “Staff A”, and nil if it’s created by “Staff B”. Your regression outcomes are listed under:
Coefficient Commonplace Error of Coefficient
Intercept 4000 1000
Staff A 800 200
(i) Interpret the that means of the intercept within the above regression. (5 marks)
(ii) Interpret the that means of the coefficient on the variable “Staff A” within the above regression. (5 marks)
(iii) Use these regression outcomes to find out the typical weekly income generated by Staff A. (5 marks)
(iv) Use your statistical coaching to carefully check whether or not or not the 2 groups generate comparable or completely different ranges of weekly income. (5 marks)
(b) Suppose that as an alternative of working the regression listed above, you as an alternative estimate the next regression:
On this regression, “Income” remains to be outlined in the identical means as earlier than, however “Staff B” is a dummy variable equal to 1 if the income is created Staff B, and nil if it was created by Staff A. On this case:
(i) Use the estimated coefficients from half (a) to find out the worth of the intercept time period on this regression (right here partially (b)). Interpret the that means of the intercept on this case. (5 marks)
(ii) Use the estimated coefficients from half (a) to find out the worth of the coefficient on the dummy variable “Staff B” on this regression (right here partially (b)). Interpret the that means of the coefficient on “Staff B” on this case. (5 marks)
