Essay HI6007 : Statistics for Business Decisions Regression Statistics Multiple – Statistics Assignment Help

Assignment Task:

Task:

Question 1 ( 7 marks)Holmes institute Students evaluation of the course they follow, askes following questions from students. Identify the type of data and measurement scale for each with relevant justifications.

• How many interactive tutorials did you attend in this semester?
• What was your group assignment grade (HD, D, C, P, F)?
• Rate the lecturer (very effective, effective, not too effective and not at all effective)
• Which campus you are registered in (Melbourne, Sydney, Brisbane or Gold coast)
• (2 marks)
• ANSWER: ** Answer box will enlarge as you type
• An investor recorded the following annual returns of one of his investments. You are required to calculate and comment on;
• Mean return.
• Variance and standard deviation of the return.
• Geometric return.
• Year 2016 2017 2018 2019 2020
• Return 15% 17% 19% 10% -5%
• (5 marks)
• ANSWER: ** Answer box will enlarge as you typeQuestion 2 (11 marks)
• Nature lovers’ association of Australia, launched a campaign to encourage paper less communication and/or recycling of used papers to save the trees to reduce global warming. Hence, many small businesses have scaled up their business such as new forms of online document exchanges and collecting used papers and cardboards from households and companies.
• Abita Recycling Ltd is one such company which is operates in Melbourne. The financial analysist of the company has estimated that the firm would make a profit if the mean weekly collection of papers and cardboards from each household exceeded 1KG. To examine the feasibility of a recycling plant, a random sample of 100 households was selected and sample mean and standard deviations are 1.1KG and 0.35KG respectively.
• Following the 6-step process of hypothesis testing, you are required to examine do this information provide sufficient evidence at 99% confidence to allow the analyst to conclude that a recycling plant would be profitable?
• ANSWER:
• Question 3 (11 marks)
• Edex limited is a renowned agricultural chemical manufacturer in Australia. They conduct many research and development in the field of Agri and Horticulture. Company wanted to examine the effect of temperature on farming of their selected range of products.
• Company has produced following results based on their data gathering.
• 15° C 35 24 36 39 32
• 25° C 30 31 34 23 27
• 35° C 23 28 28 30 31
• You are required to answer following questions;
• State the null and alternative hypothesis for single factor ANOVA to test for any significant difference in the perception among three groups. (1 marks)
• ANSWER:
• State the decision rule at 5% significance level. (2 marks)
• ANSWER:
• Calculate the test statistic. (6 marks)
• ANSWER:
• Based on the calculated test statistics, decide whether there are any significant differences between the yield based on the given temperature levels.   (2 marks)
• ANSWER:
• Note: No excel ANOVA output allowed in question3. Students need to show all the steps in calculations.
• Question 4 (7 marks)
• Melbourne Uni Lodge has decided to provide cup of cold or hot drinks for their tenants to attract them after the Covid pandemic. They have determined that mean number of cups of drinks per day is 2.00 with the standard deviation of 0.6. There will be 125 new tenants in the upcoming months.
• What is the probability that the new tenants will consume more than 240 cups of drinks per day?
• ANSWER:
• Question 5 (7 marks)
• Yummy Lunch Restaurant needs to decide the most profitable location for their business expansion. Marketing manager plans to use a multiple regression model to achieve their target. His model considers yearly revenue as the dependent variable. He found that number of people within 2KM (People), Mean household income(income), no of competitors and price as explanatory variables of company yearly revenue.
• The following is the descriptive statistics and regression output from Excel.
• Revenue People Income Competitors Price
• Mean 343965.68 5970.26 41522.96 2.8 5.68
• Standard Error 5307.89863 139.0845281 582.1376385 0.142857 0.051030203
• Median 345166.5 6032 41339.5 3 5.75
• Mode #N/A 5917 #N/A 3 6
• Standard Deviation 37532.51115 983.47613 4116.334718 1.010153 0.360838027
• Sample Variance 1408689393 967225.2984 16944211.51 1.020408 0.130204082
• Sum 17198284 298513 2076148 140 284
• Count 50 50 50 50 50
• SUMMARY OUTPUT Regression Statistics Multiple R 0.77 R Square A Adjusted R Square B Standard Error 25139.79 Observations 50.00 ANOVA   df SS MS F Significance F Regression C 40585376295 F H 3.0831E-08 Residual D 28440403984 G Total E 69025780279         Coefficients Standard Error t Stat P-value
• Intercept -68363.1524 78524.7251 -0.8706 0.3886
• People 6.4394 3.7051 I 0.0891
• Income 7.2723 0.9358 J 0.0000
• Competitors -6709.4320 3818.5426 K 0.0857
• Price 15968.7648 10219.0263 L 0.1251
• You are required to;
• Complete the missing entries from A to L in this output (2 marks)
• ANSWER:
• Derive the regression model (1 mark)
• ANSWER:
• What does the standard error of estimate tell you about the model? (1 mark)
• ANSWER:
• Assess the independent variables significance at 5% level (develop hypothesis if necessary in the analysis)? (3 marks)
• ANSWER:
• Question 6 (7 marks)
• Anita Limited has shared their annual sales revenue over the last 6 financial years from 2015 to 2020.
• Year Sales ($ 000)
• 2015 4500
• 2016 5100
• 2017 4900
• 2018 5400
• 2019 5670
• 2020 6000
• You are required to;
• Using linear trend equation forecast the sales revenue of Anita Limited for 2021. (5 marks)
• ANSWER:
• Calculate the forecasted sales difference if you use 3-period weighted moving average designed with the following weights: 2018 (0.1), 2019 (0.3) and 2020(0.6). (2 marks)
• ANSWER:
• Note: See the formula sheet on the next page. FORMULA SHEET
• K = 1 + 3.3 log10 n
• Summary Measures(n – sample size; N – Population size)
• ?= i=1NXiN X= i=1nXin p= Xns2= 1n-1i=1nxi-x2 Or s2= 1n-1i=1nxi2-nx2Or s2= 1n-1i=1nxi2-i=1nxi2n?2= 1Ni=1Nxi-µ2 Or ?2= 1Ni=1Nxi2-nµ2s~Range4 CV=?µ cv=sxLocation of the pth percentile:
• Lp= p100(n+1)IQR = Q3 – Q1
• Expected value of a discrete random variable
• Ex=?=x*f(x)Variance of a discrete random variable
• Varx=x-?2f(x)Z and t formulas:
• Z=x-??Z=x-??nZ=p-ppqnt=x-?snConfidence intervals
• Mean:180974107950x±z?/2?n0x±z?/2?nx±t?/2snProportion:
• p ± z?2p qnn= z?/22 p qB2Time Series Regression
• b1= t=1nt- tyt- yt=1nt- t2b0= Y- b1tTt= b0+ b1tANOVA:
• 180975041275 MSE=SSEnT-k0 MSE=SSEnT-k-7620091440MSTR=SSTRk-100MSTR=SSTRk-1
• 1609725107950 SST=j=1ki=1njxij-x20 SST=j=1ki=1njxij-x2-46990127000SSTR=j=1knjxj-x20SSTR=j=1knjxj-x2
• 184785020320
• F = MSTR / MSE
• 0
• F = MSTR / MSE
• SSE= j=1knj-1sj2Simple Linear Regression:
• 160972568580 b0=y-b1x00 b0=y-b1x-85725106680 y=b0+b1x0 y=b0+b1x
• -314325179070 b1=xi-xyi-yxi-x20 b1=xi-xyi-yxi-x2
• 196215160960 SST = SSR + SSE
• 0 SST = SSR + SSE
• SSE = yi-yi2SST = yi-y2SSR= yi-y2Coefficient of determination
• left106680R2= SSR/SST
• 0R2= SSR/SST
• Correlation coefficient
• r= x- xy- yx- x2y- y2 or r= XY- X YNX2- X2NY2- Y2NR2 =(rxy )2-85725137795rxy=(sign of b1)Coefficient of Determination00rxy=(sign of b1)Coefficient of Determination
• Testing for Significance
• 2305050130175s = MSE=SSEn-2s = MSE=SSEn-20142240s 2 = MSE = SSE/(n ? 2)
• s 2 = MSE = SSE/(n ? 2)
• 165671585725t=b1sb10t=b1sb1-6667676200sb1=sxi-x20sb1=sxi-x2
• 326834526035F = MSTR / MSE
• F = MSTR / MSE
• 1619250104775MSE = SSE/n-k
• MSE = SSE/n-k
• -3810095250MSR = SSR/k-1
• MSR = SSR/k-1
• Confidence Interval for ?1
• b1±t?/2sb1-66675142875y = ?0 + ?1×1 + ?2×2 + . . . + ?pxp + ?
• y = ?0 + ?1×1 + ?2×2 + . . . + ?pxp + ?
• Multiple Regression:
• -85725181610y = b0 + b1x1 + b2x2 + . . . + bpxp
• y = b0 + b1x1 + b2x2 + . . . + bpxp
• -120650619125R2 = SSR/SST
• R2 = SSR/SST
• -22860076200 Ra2=1- (1-R2)n-1n-p-10 Ra2=1- (1-R2)n-1n-p-1