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- The following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t= Years since 2006 0 1 2 3 4 5 6 7 8 9 10 K= Price 56 51 50 55 58 52 45 43 44 48 51 Make a quartic model of these data. Round the regression parameters to two decimal places.Suppose the Sherwin-Williams Company is interested in developing a simple regression model with paint sales (Y) as the dependent variable and selling price (P) as the independent variable. Complete the following worksheet and then use it to determine the estimated regression line. Sales Region Selling Price Sales ($/Gallon) (x 1000 Gal) ii xixi yiyi xixiyiyi xi2xi2 yi2yi2 1 15 160 2,400 225 25,600 2 13.5 220 2,970 182.25 48,400 3 16.5 140 2,310 272.25 19,600 4 14.5 190 2,755 210.25 36,100 5 17 120 2,040 289 14,400 6 16 160 2,560 256 25,600 7 13 210 2,730 169 44,100 8 18 150 2,700 324 22,500 9 12 220 2,640 144 48,400 10 15.5 190 2,945 240.25 36,100 Total 151 1,760 26,050 2,312 320,800 Regression Parameters Estimations Slope (ββ) -16.49 Intercept (αα) 424.98 In words, for a dollar increase in the selling price, the expected sales will increase by 2,640 gallons in a given sales region.…Suppose the Sherwin-Williams Company is interested in developing a simple regression model with paint sales (Y) as the dependent variable and selling price (P) as the independent variable. Complete the following worksheet and then use it to determine the estimated regression line. Sales Region Selling Price Sales ($/Gallon) (x 1000 Gal) ii xixi yiyi xixiyiyi xi2xi2 yi2yi2 1 15 160 2,400 225 25,600 2 13.5 220 2,970 182.25 48,400 3 16.5 140 2,310 272.25 19,600 4 14.5 190 2,755 210.25 36,100 5 17 120 2,040 289 14,400 6 16 160 2,560 256 25,600 7 13 210 2,730 169 44,100 8 18 150 2,700 324 22,500 9 12 210 2,520 144 44,100 10 15.5 190 2,945 240.25 36,100 Total 151 1,750 2,312 What is the estimate of the standard deviation of the estimated slope (sbsb)? 2.627 3.173 2.877 Can you reject the hypothesis (at the 0.05 level of significance) that there is no relationship (i.e., β=0β=0) between the…
- Based on the data shown below, calculate the regression line.Regression Equation: Enter the equation in slope-intercept form (y=mx+b)(y=mx+b) with parameters accurate to three decimal places. x y 2 10.3 3 11.41 4 9.92 5 12.93 6 12.34 7 9.85 8 12.36 9 11.87 10 11.68 11 12.49 12 11.4To fit a simple linear regression model to the data and to provide its equation (d = a*t + b), along with R2 Day Date Weekday Daily Demand Weekend 1 4/25/2016 Mon 297 0 2 4/26/2016 Tue 293 0 3 4/27/2016 Wed 327 0 4 4/28/2016 Thu 315 0 5 4/29/2016 Fri 348 0 6 4/30/2016 Sat 447 1 7 5/1/2016 Sun 431 1 8 5/2/2016 Mon 283 0 9 5/3/2016 Tue 326 0 10 5/4/2016 Wed 317 0 11 5/5/2016 Thu 345 0 12 5/6/2016 Fri 355 0 13 5/7/2016 Sat 428 1 14 5/8/2016 Sun 454 1 15 5/9/2016 Mon 305 0 16 5/10/2016 Tue 310 0 17 5/11/2016 Wed 350 0 18 5/12/2016 Thu 308 0 19 5/13/2016 Fri 366 0 20 5/14/2016 Sat 460 1 21 5/15/2016 Sun 427 1 22 5/16/2016 Mon 291 0 23 5/17/2016 Tue 325 0 24 5/18/2016 Wed 354 0 25 5/19/2016 Thu 322 0 26 5/20/2016 Fri 405 0 27 5/21/2016 Sat 442 1 28 5/22/2016 Sun 454 1 29 5/23/2016 Mon 318 0 30 5/24/2016 Tue 298 0 31 5/25/2016 Wed 355 0 32 5/26/2016 Thu 355 0 33 5/27/2016 Fri 374 0 34 5/28/2016 Sat 447 1 35 5/29/2016…given the information below: Row Education Income in in Years 2015 Dollars 1 7 22587 2 10 28305 3 12 40196 4 13 49483 5 14 54483 6 16 78073 7 18 99540 8 19 155646 9 21 125310 1. Estimate the regression equation Income = a + b(Education). 2. What is the predicted increase in Income for a one-year increase in Education? 3. What do you predict Income to be for a person who has 17 years of education? 4. How much of the variation in Income is explained (or accounted for) by Education?
- The following are data on the average weekly profits(in $1,000) of five restaurants, their seating capacities, andthe average daily traffic (in thousands of cars) that passestheir locations: Seating Traffic Weekly netcapacity count profitx1 x2 y120 19 23.8200 8 24.2150 12 22.0180 15 26.2240 16 33.5 (a) Assuming that the regression is linear, estimate β0, β1,and β2.(b) Use the results of part (a) to predict the averageweekly net profit of a restaurant with a seating capacityof 210 at a location where the daily traffic count averages14,000 cars.An unknown metal has been found and the following experimental results have been tabulated in the table below. The table contains the grams of the unknown metal and the volume in milliliters of water displacement. Find a linear model that expresses mass as a function of the volume. grams Volume in ml 17 130.8 19.5 150 22 171 24.5 196.2 27 207.7 29.5 233.9 32 256.2 A) Write the linear regression equation for the data in the chart. Volume = x+ where x is the grams of the unknown metal. Round your answers to 3 decimal places B) If the mass of an unknown metal is 15, using your un-rounded regression equation find its predicted volume. Round your answer to 1 decimal place. mLConsider the following estimated regression model relating annual salary to years of education and work experience. Estimated Salary=11,656.59+2985.74(Education)+1180.42(Experience)Estimated Salary=11,656.59+2985.74(Education)+1180.42(Experience) Suppose two employees at the company have been working there for five years. One has a bachelor's degree (88 years of education) and one has a master's degree (1010 years of education). How much more money would we expect the employee with a master's degree to make
- Shown below is a portion of a computer output for a linear regression analysis relating y (demand in units) and x (unit price in $). Coefficient Standard Error t-statistic p-value Intercept 80.390 3.102 25.916 0.000 x –2.137 0.248 ? 0.000 Source of Variation Sum of squares Degrees of freedom Mean square F-statistic p-value Regression 5048.818 1 5048.818 ? ? Error ? 46 ? Total 8181.479 47 We are interested in determining whether or not demand and unit price are linearly related using a significance level α = 0.05 . a. Fully interpret the meaning of the estimated coefficient of x in this estimated linear regression equation. b. Complete the missing values in the regression output tables above. c.Calculate the coefficient of determination, r2, and fully interpret its meaning in this context. Be very specific.Suppose the Sherwin-Williams Company has developed the following multiple regression model, with paint sales Y (x 1,000 gallons) as the dependent variable and promotional expenditures A (x $1,000) and selling price P (dollars per gallon) as the independent variables. Y=α+βaA+βpP+ε�=�+���+���+� Now suppose that the estimate of the model produces following results: α=344.585�=344.585, ba=0.106��=0.106, bp=−12.112��=−12.112, sba=0.155�ba=0.155, sbp=4.312�bp=4.312, R2=0.764�2=0.764, and F-statistic=12.593F-statistic=12.593. Note that the sample consists of 10 observations. According to the estimated model, holding all else constant, a $1,000 increase in promotional expenditures sales by approximately gallons. Similarly, a $1 increase in the selling price sales by approximately gallons. Which of the independent variables (if any) appears to be statistically significant (at the 0.05 level) in explaining paint sales? Check all that apply. Selling price (P)…A study of the amount of rainfall and the quantity of air pollution removed produced the following data shown in table below: Daily Rainfall x (0.01 cm) Particulate Removed y (μg/m3) 7 126 7.9 129.3 7.5 125.3 9.2 120.2 10.8 116.7 5.8 119.2 5.6 138.7 2.7 147.5 9.2 110.3 Plot a scatter diagram. Find the equation of the regression line to predict (y) for the particulate removed from the amount of daily rainfall.
