9. Use the formula (imA)+ = ker(AT) to prove the equation rank(A) = rank(AT).
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- The file P13_22.xlsx contains total monthly U.S. retail sales data. While holding out the final six months of observations for validation purposes, use the method of moving averages with a carefully chosen span to forecast U.S. retail sales in the next year. Comment on the performance of your model. What makes this time series more challenging to forecast?Tucson Machinery, Inc., manufactures numerically controlled machines (NCM), which sell for an average price of $12 million each. Sales for these NCMs for the past two years were as follows: Quantity (units) Quantity (units) Quarter Last year ||| III IV 12 18 20 24 Quarter This year | || ||| IV 20 24 28 32 Find the equation of a simple linear regression line using Excel, in the format of Y=a+bX. Keep two decimals of a and b. Forecast the first quarter sales for next year. Keep two decimals.PLEASE SHOW WORK SO I CAN UNDERSTAND
- DFC Company has recorded the past years sales for the company: Year(t) Sales(x) (in Million Pesos) 2011(1) 2012(2) 2013(3) 2014(4) 2015(5) 2016(6) 2017(7) 2018(8) 2019(9) 2020(10) 219 224 268 272 253 284 254 278 282 298 Use the naïve model. Compute for MAE and MSE Use a three period moving average. Compute for the MAE and MSE Use the simple exponential smoothing to make a forecasting table. Compute the MAE and MSE of the forecasts. Alpha = 0.1 Use the least square method to make the forecasting table. Compute the MAE and MSE *** Use excel or r programmingPlease do not give solution in image format thankuWhat are measurement scales, their types. Explain each in detail with proper explanation and examples. The sales tax officer in a district has reported that the average sales of the 50 business firms that dealt with during last year amounted to Rs. 36,000 /-with a standard deviatonof Rs10,000 / -. Assuming that the sales of these firms were normally distributed find: (For z-values, use the z table from internet) (a) The no. of business firms the sales of which were over Rs. 40,000 /- (b) The % of business firms the sales of which were likely to range between Rs. 30,000 and Rs40,000
- 7do fast.A 45 kW rated solar power system has its power output and the Solar irradiance on the PV system measured during daylight hours over a day. Based on the following data, create a scatter plot of the power output of the PV system vs the solar irradiance and comment on the relationship between the two. Based on the data, can you tell which season this day was in? Solar Irradiance on the PV system (kW/m²) 0 0.079 0.333 0.571 0.751 0.86 0.914 0.93 0.904 0.803 0.606 0.345 0.054 Power output from the PV system (kW) 0 3.098 12.438 20.124 25.703 28.498 29.587 29.69 28.798 26.264 20.434 12.223 2
- 5) Consider the following tableau. Basic | Coefficients Vars x2 X3 X4 Const 1 -1 -3 -2 -1 1 -2 4 1 3 1 3 A) Label the basic variables (blank entries in the first column). B) Identify the entering (nonbasic) variable. C) Identify the exiting (basic) variable corresponding to your choice in part B. D) Perform a pivot based on your choices in B and C.3. Attendance at Los Angeles' newest Disney like attraction, Vacation World has been as follows: Quarter Guests Quarter Guests (in Thousands) (in Thousands) 2017 Q1 73 Q3 124 Q2 104 Q4 52 Q3 168 2019 Q1 89 Q4 74 Q2 146 2018 Q1 65 Q3 205 Q2 82 Q4 98 a. Graph the data. (Use Excel) b. Compute seasonal indices using all the data. (Solve manually)To better plan for future growth of the restaurant, Karen needs to develop a system that will enable her to forecast food and beverage sales by month for up to one year in advance. Table shows the value of food and beverage sales ($1000s) for the first three years of operation. Food and Beverage Sales for the Vintage Restaurant ($1000s) Month First Year Second Year Third Year January 242 263 282 February 235 238 255 March 232 247 265 April 178 193 205 May 184 193 210 June 140 149 160 July 145 157 166 August 152 161 174 September 110 122 126 October 130 130 148 November 152 167 173 December 206 230 235 Managerial Report Perform an analysis of the sales data for the Vintage Restaurant. Prepare a report for Karen that summarizes your findings, forecasts, and recommendations. Include the following: A time series plot. Comment on the underlying pattern in the time series.…