Management proposed the following regression model to predict sales at a fast-food outlet.y=B₁ + B₁x₁ + B₂x₂ + Bzx3 +6wherex₁ = number of competitors within one mileX₂= population within one mile (1,000s)x3 =[1 if drive-up window presentlo otherwisey = sales ($1,000s).The following estimated regression equation was developed after 20 outlets were surveyed.9-10.1-4.2x₁ + 6.8x₂ + 15.3x3(a) What is the expected amount of sales (in dollars) attributable to the drive-up window?$(b) Predict sales (in dollars) for a store with four competitors within one mile, a population of 8,000 within one mile, and no drive-up window.$(c) Predict sales (in dollars) for a store with one competitor within one mile, a population of 3,000 within one mile, and a drive-up window.$

The regression model to predict sales at a fast food outlet based on 20 outlets is given as:where,…

Answered: gement proposed the following…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Personal wealth tends to increase with age as older individuals have had more opportunities to earn and invest than younger individuals. The following data were obtained from a random sample of eight individuals and records their total wealth (Y) and their current age (X). Data provided in the image. a. State the estimated regression line and interpret the slope coefficient.b. What is the estimated total personal wealth when a person is 50 years old?c. What is the value of the coefficient of determination? Interpret it. d. Test whether there is a significant relationship between wealth and age at the 10%significance level. Perform the test using the following six steps. Step 1. Statement of the hypothesesStep 2. Standardised test statisticStep 3. Level of significanceStep 4. Decision. Step 5. Calculation of test statistic. Step 6. Conclusion Please solve the d) part only.
1.
The commercial division of a real estate firm is conducting a regression analysis of the relationship between x, annual gross rents (in thousands of dollars), and y, selling price (in thousands of dollars) for apartment buildings. Data were collected on several properties recently sold and the following computer output was obtained. The regression equation is Y = 20.0 + 7.25 X Predictor Сoef SE Coef Constant 20.000 3.2213 6.21 7.250 1.3628 5.29 Analysis of Variance SOURCE DF SS Regression 1 41,587.1 Residual Error 7 Total 8 51,984.5 a. How many apartment buildings were in the sample? b. Write the estimated regression equation (to 2 decimals if necessary). + c. What is the value of sb1 (to 4 decimals)?
The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.5 8.2 6.9 3.3 2.8 2.2 2.6 0.6 yy 13.7 10.9 10.2 7 6.1 5.8 6.3 4.2 xx = thousands of automatic weaponsyy = murders per 100,000 residentsThis data can be modeled by the equation y=0.87x+3.9.y=0.87x+3.9. Use this equation to answer the following;A) How many murders per 100,000 residents can be expected in a state with 2.5 thousand automatic weapons?Answer = Round to 3 decimal places.B) How many murders per 100,000 residents can be expected in a state with 5.2 thousand automatic weapons?Answer = Round to 3 decimal places. Submit QuestionQuestion 17
Data from 147 colleges from 1995 to 2005 (Lee,2008) were tested to predict the endowments (in billions) to a college from the average SAT score of students attending the college. The resulting regression equation was Y = -20.46 + 4.06 (X). This regression indicates that: a. for every one-point increase in SAT scores, a college can expect 4.06 billion more in endowments. b. most colleges have very high endowments. c. for every one-point increase in SAT scores, a college can expect 20.46 billion fewer in endowments. d. for every one-dollar increase in endowments, the college can expect a half-point increase in SAT scores.
R1
3. A study of beer consumption using the annual data from 1980 -2001 produced the following regression: Y = 0.41 +0.052.X₁; −0.047X2; +0.032X3; −0.018X4i (0.027) (0.011) (0.009) (0.008) (0.009) R² = 0.94 F = 66.58 DW statistic=1.32, figures in the brackets are standard errors Where: Y₁ = Annual aggregate beer consumption in year t (billion pints) X₁₁ = Real disposable income income in year t ($ billions at 2001 prices) X2i = Price of beer in year t (index number with 2001 = 100) X31 Price of wine and sprits in year t (index number with 2001 = 100) = X4₁ = Price of cigarettes in year t (index number 2001 = 100) (a) What is the effect of a change in the price of beer on beer consumption? Does it have the correct sign? Explain. (b) Comment on the signs of the other three coefficients. Are they as expected? (c) Tests the significance of the coefficients on each of the variables Xit i = 1, 2, 3, 4. What assumptions have you made in carrying out these tests? (d) What conclusion do you draw…
The City of Bellmore’s police chief believes that maintenance costs on high-mileage police vehicles are much higher than those costs for low-mileage vehicles. If high-mileage vehicles are costing too much, it may be more economical to purchase more vehicles. An analyst in the department regresses yearly maintenance costs (Y) for a sample of 200 police vehicles on each vehicle’s total mileage for the year (X). The regression equation finds: Y = $50 + .030X with a r2 of .90 What is the IV? What is the DV? If the mileage increases by one mile, what is the predicted increase in maintenance costs? If a vehicle’s mileage for the year is 50,000, what is its predicted maintenance costs? What does an r2 of .90 tell us? Is this a strong or weak correlation? How can you tell?
The following data on x maternal age in years of the young birth mothers and y = weight of baby born in grams summarizes the result of a study. Assume that a simple linear regression model y = Bo + B1x + e is an appropriate model for the study. x-bar = 17 (avg of x's) y-bar = 3004.1 (avg of y's) SSx = 20 SSxy %3D 4903 SSw 1539182.9 n 10 Calculate the value of s-(standard error of regression) and enter the answer to the nearest tenth (1 decimal place).
Solvent cement is used to join PVC joints. Researchers are interested in predicting the amount of time needed for the joint to set (measured in hours) as it is related to the temperature measured in degrees F for 4 to 8-inch diameter pieces. A random sample of PVC joints was taken and a linear regression model was found. Use the following output and the fact that R2 = 0.965 to answer the following questions. 1. Find the equation of the regression line. 2. Interpret the slope in the words of the problem. 3. Find the Coefficient of Determination and interpret in the words of the problem
The following equation describes the relationship between output and labor input at a sample of work stations in a manufacturing plant ŷ = 2.35+2.20X. Suppose, for a selected workstation, the labor input is 5, the predicted output is?
Define both x and y in all problems. x is the cause, and y is the effect. This is the most important step when doing linear regression, otherwise, all the remanding parts will be wrong.

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