Question 1The following table of values gives a company's annual profits in millions of dollars. Rescale the data so that the year 2005 corresponds to x = 0.YearProfits (in millions of dollars)Find the quadratic regression model for this data.a) Oy = -0.4x² +2.06x+62.5b) y = -1.4426x² +9.2207 x + 53.1870c)y = -1.3554 x² +11.0761 x + 43.99d) Oy-1.3554 x² +8.3654x + 53.7107e) y = -2.4286 x² + 12.0143 x + 52.4229f) None of the above2005 2006 2007 2008 200951.8 63.4 66.3 65.8 62.1201063.8Review Later

Make a table for the given data as follows Year Profit in millions 0 51.8 1 63.4 2 66.3 3…

Answered: The following table of values gives a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Q: The US Box Office Gross profit was recorded for the first eleven weekends after the release of a major motion picture. For the dataset posted below this question, construct a scatterplot with the weekend as the horizontal axis and US Gross (in millions of dollars) as the vertical axis. Conduct an analysis of the Residuals using the Data Analysis ToolPak Regression tool. Comment on whether the assumptions of linear regression have been met. (Please solve this in Excel) Weekend US Gross (millions $) 1 47.7 2 25 3 11.35 4 7 5 4.68 6 3.02 7 1.34 8 0.72 9 0.49 10 0.31 11 0.2
Use the time/tip data from the table below, which includes data from New York City taxi rides. (The distances are in miles, the times are in minutes, the fares are in dollars, and the tips are in dollars.) Find the regression equation, letting time be the predictor (x) variable. Find the best predicted tip for a ride that takes 22 minutes. How does the result compare to the actual tip amount of $5.05? Distance 1.80 8.51 1.40 1.65 12.71 1.02 1.32 Time Fare Tip 0.68 8.00 6.00 25.00 31.00 18.00 11.00 27.00 8.00 16.30 31.75 12.30 9.80 36.80 7.80 7.80 6.30 1.50 2.98 2.46 1.96 0.00 2.34 0.00 1.89 The regression equation is ŷ = + (x. (Round the y-intercept to two decimal places as needed. Round the slope to four decimal places as needed.)
A real estate company wants to study the relationship between house sales prices and some important predictors of sales prices. Based on data from recently sold homes in the space, the following variables are used in a multiple regression model. y = sales price (in thousands of dollars) x₁ = total floor area (in square feet) x₂ = number of bedrooms x3 distance to nearest high school (in miles) = The estimated model is as follows. =76+0.098x₁ +16x₂ - 8x3 Answer the questions below for the interpretation of the coefficient of X₂ in this model. (a) Holding the other variables fixed, what is the average change in sales price for each additional bedroom in a house? dollars (b) Is this change an increase or a decrease? O increase O decrease X
The owner of Showtime Movie Theaters, Inc., used multiple regression analysis to predict gross revenue (y) as a function of television advertising (x 1) and newspaper advertising (x 2). The estimated regression equation was Weekly Gross Revenue ($1000s) Televison Advertising ($1000s) Newspaper Advertising ($1000s) 97 6 1.5 91 3 2 95 5 2.5 93 3.5 2.5 96 4 4.3 94 4.5 2.3 95 3.5 4.2 95 4 3.5 ŷ = 82.5 + 2.01 x 1 + 1.26 x 2The computer solution provided SST = 24 and SSR = 22.876. Compute R 2 and R a 2 (to 3 decimals). R 2 R a 2 When television advertising was the only independent variable, R 2 = 0.551 and R a 2 = 0.476. Are the multiple regression analysis results preferable?
The accompanying data are the shoe sizes and heights (in inches) of 14 men. Find the equation of the regression line. Then construct a scatter plot of the data and draw the regression line. Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. If the x-value is not meaningful to predict the value of y, explain why not. (a) x=11.5 (b) x=8.0 (c) x=15.5 (d) x= Shoe Size, x Height, y8.5 66.09.0 69.09.0 67.59.5 70.510.0 70.510.0 72.010.5 71.510.5 70.011.0 71.011.0 71.511.0 73.012.0 73.012.0 74.012.5 73.5 The equation of the regression line is y= ____x +____
The scatter plot below shows the average cost of a designer jacket in a sample of years between 2000 and 2015. The least squares regression line modeling this data is given by yˆ=−4815+3.765x. A scatterplot has a horizontal axis labeled Year from 2005 to 2015 in increments of 5 and a vertical axis labeled Price ($) from 2660 to 2780 in increments of 20. The following points are plotted: (2003, 2736); (2004, 2715); (2007, 2675); (2009, 2719); (2013, 270). All coordinates are approximate. Interpret the slope of the least squares regression line. Select the correct answer below: 1.The average cost of a designer jacket decreased by $3.765 each year between 2000 and 2015. 2.The average cost of a designer jacket increased by $3.765 each year between 2000 and 2015. 3.The average cost of a designer jacket decreased by $4815 each year between 2000 and 2015. 4. The average cost of a designer jacket increased by $4815 each year between 2000 and…
Researchers studying tigers collected data on the length (in meters) and weight (in kilograms) of the animals. Is there statistically significant evidence that the length of tigers is related to their weight?
Use the screenshot attached to answer question thanks What is the per unit variable cost? Round to 1 decimal place. $ per sleeping bag
Draw the regression line for the following equation: Y = -3 + (1) X Show your calculation for a low and high value on the predictor value.
The following table of values gives a company's annual profits in millions of dollars. Rescale the data so that the year 2005 corresponds to x = 0. Year 2005 2006 2007 2008 2009 2010 Profits (in millions of dollars) 51.8 63.4 66.3 65.8 62.1 63.8 Find the exponential regression model for this data.
Use the time/tip data from the table below, which includes data from New York City taxi rides. (The distances are in miles, the times are in minutes, the fares are in dollars, and the tips are in dollars.) Find the regression equation, letting time be the predictor (x) variable. Find the best predicted tip for a ride that takes 20 minutes. How does the result compare to the actual tip amount of $4.55? Distance 0.68 2.47 12.71 1.80 1.02 8.51 1.32 1.40 6.00 18.00 27.00 25.00 8.00 31.00 8.00 18.00 6.30 14.30 36.80 16.30 7.80 31.75 7.80 12.30 1.89 4.29 0.00 1.50 2.34 2.98 0.00 2.46 Time Fare Tip The regression equation is y=+ X (Round the y-intercept to two decimal places as needed. Round the slope to four decimal places as needed.) The best predicted tip for a ride that takes 20 minutes is $ (Round to the nearest cent as needed.) How does the result compare to the actual tip amount of $4.55? O A. The best predicted value is close to the actual tip of $4.55. O B. The best predicted value…
The table below shows the average weekly wages (in dollars) for state government employees and federal government employees for 10 years. Construct and interpret a 98% prediction interval for the average weekly wages of federal government employees when the average weekly wages of state government employees is $878.The equation of the regression line is y=1.342x+55.816. Wages [state]- 712, 746, 786, 803, 841, 879, 918, 926, 954, 979 Wages [federal]- 1,024, 1,048, 1,098, 1,135, 1,195, 1,240, 1,270, 1,299, 1,340, 1,376 Construct and interpret a 98% prediction interval for the average weekly wages of federal government employees when the average weekly wages of state government employees is $878. Select the correct choice below and fill in the answer boxes to complete your choice. (Round to the nearest cent as needed.) PICK THE CORRECT ANSWER [A] We can be 98% confident that when the average weekly wages of state government employees is $878, the average weekly wages of…

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