Question Assignment 1
\nSuppose 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:
\ncase:
\n(i) \u201cIncome\u201d is the income (per worker) per week for every retailer in 1000’s of dollars
\n(ii) \u201cDimension of Retailer\u201d is the world of the shop\u2019s floorplan (in sq. metres).
\n(iii) \u201cDistance to Nearest Main Highway\u201d is the space (in tons of of metres) to the closest Four-lane (or bigger) highway resulting in the shop.
\n(iv) \u201cMarket Dimension\u201d is the variety of folks, in 1000’s, who reside out there served by every retailer.
\nThe regression outcomes from the info you\u2019ve acquired are displayed under:
\nCoefficient Commonplace Error of Coefficient
\nIntercept Four 1
\nDimension of Retailer zero.1 zero.02
\nDistance to Nearest Main Highway \u20131 zero.25
\nMarket Dimension zero.5 zero.1
\nThe questions associated to those outcomes are displayed on the next web page.
\n(a) What’s the correct, technical interpretation of the coefficient on \u201cDimension of Retailer\u201d within the a number of regression? (5 marks)
\n(b) On this a number of regression setting, how would you check the speculation that the impact of \u201cDimension of Retailer\u201d on revenues was zero on the 5% stage of significance for all markets during which your organization operates? (5 marks)
\n(c) Once more, on this a number of regression setting, check (on the 5% stage of significance) the speculation that the variable \u201cDistance to Nearest Main Highway\u201d no impact on a retailer\u2019s revenues.
\n(5 marks)
\n(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 \u201cPromoting Price range\u201d, and your regression is now specified as:<\/p>\n
Utilizing this new regression, you acquire the next outcomes:
\nCoefficient Commonplace Error of Coefficient
\nIntercept Four 1
\nDimension of Retailer zero.01 zero.02
\nDistance to Nearest Main Highway \u20131 zero.25
\nMarket Dimension zero.5 zero.1
\nPromoting Price range 2 zero.Four
\nOn this case, check the speculation that the impact of \u201cDimension of Retailer\u201d on revenues was zero on the 5% stage of significance for all markets during which your organization operates? (5 marks)
\n(e) Clarify why the coefficient worth on \u201cDimension of Retailer\u201d and the speculation check on this coefficient is completely different partially (d) than partially (a) and (b). (10 marks)
\nQuestion Assignment 2
\nYou\u2019ve 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:
\nOn this case:
\n(v) \u201cValue\u201d is the value of the laptop computer (in dollars)
\n(vi) \u201cDimension of display screen\u201d is the world, in sq. centimetres, of the laptop computer\u2019s display screen.
\n(vii) \u201cProcessor Pace\u201d is the pc\u2019s processing pace in GHz. (viii) \u201cRAM\u201d is pc\u2019s reminiscence in GB.
\nThe regression outcomes from the info analyzed by the inner analysis workforce are displayed under:
\nCoefficient Commonplace Error of the Coefficient
\nIntercept 500 100
\nDimension of display screen \u20135 2
\nProcessor Pace 200 50
\nRAM 100 10
\nCommonplace Error of the Regression = 150
\n(a) Present a definition of the coefficient on \u201cProcessor Pace\u201d, 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)
\n(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)
\n(Please see the next web page for the following a part of this Question Assignment)
\n(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:<\/p>\n
On this case, \u201cWeight\u201d is the burden of the laptop computer (in grams). The outcomes from this regression are displayed under:
\nCoefficient Commonplace Error of the Coefficient
\nIntercept 500 100
\nDimension of display screen \u20131 2
\nProcessor Pace 200 50
\nRAM 100 10
\nWeight \u20132 zero.5
\nCommonplace Error of the Regression = 100
\nOn this case, the coefficient on \u201cDimension of Display screen\u201d modified on this regression in comparison with the regression partially (a). How can you clarify this coefficient\u2019s change, whereas incorporating the correlation between \u201cDimension of Display screen\u201d and \u201cWeight\u201d into your reply? (10 marks)
\n(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)
\nQuestion Assignment three
\n(a) You work for a giant firm that needs to match the efficiency of two gross sales groups
\n(we\u2019ll name them \u201cStaff A\u201d and \u201cStaff B\u201d) 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:<\/p>\n
On this case, \u201cIncome\u201d represents the weekly income (in dollars) generated by the gross sales workforce, and \u201cStaff A\u201d is a dummy variable equal to 1 if the income is created by \u201cStaff A\u201d, and nil if it\u2019s created by \u201cStaff B\u201d. Your regression outcomes are listed under:
\nCoefficient Commonplace Error of Coefficient
\nIntercept 4000 1000
\nStaff A 800 200
\n(i) Interpret the that means of the intercept within the above regression. (5 marks)
\n(ii) Interpret the that means of the coefficient on the variable \u201cStaff A\u201d within the above regression. (5 marks)
\n(iii) Use these regression outcomes to find out the typical weekly income generated by Staff A. (5 marks)
\n(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)
\n(b) Suppose that as an alternative of working the regression listed above, you as an alternative estimate the next regression:<\/p>\n
On this regression, \u201cIncome\u201d remains to be outlined in the identical means as earlier than, however \u201cStaff B\u201d 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:
\n(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)
\n(ii) Use the estimated coefficients from half (a) to find out the worth of the coefficient on the dummy variable \u201cStaff B\u201d on this regression (right here partially (b)). Interpret the that means of the coefficient on \u201cStaff B\u201d on this case. (5 marks)<\/p>\n","protected":false},"excerpt":{"rendered":"
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