Almost all U.S. light-rail systems use electric cars that run on tracks built at street level. The Federal Transit Administration claims light-rail is one of the safest modes of travel, with an accident rate of .99 accidents per million passenger miles as compared to 2.29 for buses. The following data show the miles of track and the weekday ridership in thousands of passengers for six light-rail systems.

1. Use these data to develop an estimated regression equation that could be used to predict the ridership given the miles of track.
   
   Compute b₀ and b₁ (to 2 decimals).
   b₁  
   b₀  
   
   Complete the estimated regression equation (to 2 decimals).
   =  +  x
   
2. Compute the following (to 1 decimal):

   SSE
   SST
   SSR
   MSE

   
   
3. What is the coefficient of determination (to 3 decimals)? Note: report r² between 0 and 1.
   
   
   Does the estimated regression equation provide a good fit?
   SelectYes, it even provides an excellent fitYes, it provides a good fitNo, it does not provide a good fitItem 10
   
4. Develop a 95% confidence interval for the mean weekday ridership for all light-rail systems with 30 miles of track (to 1 decimal).
   (  ,  )
   
5. Suppose that Charlotte is considering construction of a light-rail system with 30 miles of track. Develop a 95% prediction interval for the weekday ridership for the Charlotte system (to 1 decimal).
   (  ,  )
   
   Do you think that the prediction interval you developed would be of value to Charlotte planners in anticipating the number of weekday riders for their new light-rail system?
   SelectYes, because this interval has high accuracyYes, because this interval has high confidenceYes, because this interval has both high accuracy and high confidenceNo, because this interval is too wideNo, because this interval has low confidence

Almost all U.S. light-rail systems use electric cars that run on tracks built at street level. The Federal Transit Administration claims light-rail is one of the safest modes of travel, with an accident rate of .99 accidents per million passenger miles as compared to 2.29 for buses. The following data show the miles of track and the weekday ridership in thousands of passengers for six light-rail systems.

1. Use these data to develop an estimated regression equation that could be used to predict the ridership given the miles of track.
   
   Compute b₀ and b₁ (to 2 decimals).
   b₁ =
   b₀ =
   
   Complete the estimated regression equation (to 2 decimals).
   
   
2. Compute the following (to 1 decimal):

   SSE	=
   SST	=
   SSR	=
   MSE	=

   
   
3. What is the coefficient of determination (to 3 decimals)? Note: report r² between 0 and 1.
   
   
   Does the estimated regression equation provide a good fit?
   SelectYes, it even provides an excellent fitYes, it provides a good fitNo, it does not provide a good fitItem 10
   
4. Develop a 95% confidence interval for the mean weekday ridership for all light-rail systems with 30 miles of track (to 1 decimal).
   (  ,  )
   
5. Suppose that Charlotte is considering construction of a light-rail system with 30 miles of track. Develop a 95% prediction interval for the weekday ridership for the Charlotte system (to 1 decimal).
   (  ,  )
   
   Do you think that the prediction interval you developed would be of value to Charlotte planners in anticipating the number of weekday riders for their new light-rail system?
   SelectYes, because this interval has high accuracyYes, because this interval has high confidenceYes, because this interval has both high accuracy and high confidenceNo, because this interval is too wideNo, because this interval has low confidenceItem 15

GBA 306 Statistical Methods of Business II – Case Study – Indiana Real Estate

Ann Perkins, a realtor in Brownsburg, Indiana, would like to use estimates from a multiple regression model to help prospective sellers determine a reasonable asking price for their homes. She believes that the following four factors influence the asking price (Price) of a house:
1)   The square footage of the house (SQFT)
2)   The number of bedrooms (Bed)
3)   The number of bathrooms (Bath)
4)   The lot size (LTSZ) in acres
She randomly collects online listings for 50 single-family homes. The data file is located in the Blackboard “Case Study Indiana Real Estate Data File Excel” within the Case Study folder.

Requirements and associated point values:
.
Part 2 – Estimate and interpret a multiple regression model where the asking price is the response variable and the other four factors are the explanatory variables.
The end result should be a Excel Regression Output
SUMMARY OUTPUT                  
                      
Regression Statistics                  
Multiple R                      
R Square                      
Adj. R Square                      
Standard Error                      
Observations                      
                      
ANOVA                      
    Df   SS   MS   F   Significance F  
Regression                      
Residual                      
Total                      
                      
    Coefficients   Standard Error   t Stat   P-value   Lower 95%   Upper 95%
Intercept                      
SQFT                      
Bed                      
Bath                      
LTSZ                      

Also provide the estimate model equation: Price =
A total of 40 points will be assigned to Part 2.

Part 3 – Interpret the resulting coefficient of determination.
A total of 20 points will be assigned to Part 3.

Price   SQFT   Bed   Bath   LTSZ
399900   5.026   4   4.5   0.3
375000   3.2   4   3   5
372000   3.22   5   3   5
370000   4.927   4   4   0.3
325000   3.904   3   3   1
325000   2.644   3   2.5   5
319500   5.318   3   2.5   2.5
312900   3.144   4   2.5   0.3
299900   2.8   4   3   5
294900   3.804   4   3.5   0.2
269000   3.312   5   3   1
250000   3.373   5   3.5   0.2
249900   3.46   2   2.5   0.6
244994   3.195   4   2.5   0.2
244900   2.914   3   3   0.3
239900   2.881   4   5   0.3
234900   1.772   3   2   3.6
234000   2.248   3   2.5   0.3
229900   3.12   5   2.5   0.2
219900   2.942   4   2.5   0.2
209900   3.332   4   2.5   0.2
209850   3.407   3   2.5   0.3
206900   2.092   3   2   0.3
200000   3.859   4   2   0.2
194900   3.326   4   2.5   0.1
184900   1.874   3   2   0.5
179900   1.892   3   1.5   0.7
179500   2.5   4   2.5   0.5
165000   2.435   4   2.5   0.4
159900   2.714   3   2.5   0.2
159900   1.85   3   2.5   0.5
155000   3.068   4   3.5   0.2
154900   2.484   4   2.5   0.3
152000   1.529   4   2   0.4
149900   2.876   4   2.5   0.2
148500   2.211   4   2.5   0.1
146900   1.571   3   2   0.2
145500   1.503   4   2   0.5
144900   1.656   3   2   0.5
144900   1.521   3   2   0.6
139900   1.315   3   2   0.2
137900   1.706   3   2   0.3
132900   2.121   4   2.5   0.1
129900   1.306   3   2   0.5
129736   1.402   3   2   0.5
125000   1.325   3   2   0.3
119500   1.234   3   2   0.2
110387   1.292   3   1   0.2
106699   1.36   3   1.5   0.1
102900   1.938   3   1   0.1
              
              

2. The New York Times reported that the average time to download the homepage from the IRS website was 0.8 seconds. Suppose the download time was normally distributed with standard deviation of 0.2 seconds. If random samples of 30 download times are selected,

a. what proportion of sample means will be less than 0.75 seconds

b. what proportion of the sample means will be between 0.7 and 0.9 seconds c. 90% of sample means will be less than what value?

A tire company finds the lifespan for one brand of its tires is normally distributed with a mean of 48,400 miles and a standard deviation of 5000 miles.

If the manufacturer is willing to replace no more than 10% of the tires, what should be the approximate number of miles for a warranty?

What is the probability that a tire will last more than 52,000 miles?  

What is the probability that a mean of 25 tires will last less than 47,000 miles?

The mean gas mileage for a hybrid car is 57 miles per gallon. Suppose that the gasoline mileage is approximately normally distributed with a standard deviation of 3.5 miles per gallon. ​

(a) What proportion of hybrids gets over 61 miles per​ gallon?

(b) What proportion of hybrids gets 52 miles per gallon or​ less?

(c) What proportion of hybrids gets between 59 and 62 miles per​ gallon?

(d) What is the probability that a randomly selected hybrid gets less than 46 miles per​ gallon?

Chubbyville purchases a delivery van for $24,100. Chubbyville estimates a four-year service life and a residual value of $1,900. During the four-year period, the company expects to drive the van 104,000 miles. 1. Straight-line. 2. Double-declining-balance. (Round your depreciation rate to 2 decimal places. Round your final answers to the nearest whole dollar.) 3. Actual miles driven each year were 24,000 miles in Year 1; 32,000 miles in Year 2; 22,000 miles in Year 3; and 24,000 miles in Year 4. Note that actual total miles of 102,000 fall short of expectations by 2,000 miles. Calculate annual depreciation for the four-year life of the van using activity-based. (Round your depreciation rate to 2 decimal places. Round your final answers to the nearest whole dollar.)

Next month there will a marathon. Ali, Mustafa, Ahmad, and Sami are friends and preparing for it. Each day of the week, they run a certain number of miles and write them into a notebook. At the end of the week, they would like to know the number of miles run each day, the total miles for the week, and average miles run each day.

Write a program to help them analyze their data. Your program must contain:

• parallel arrays: an array to store the names of the runners and
• a two-dimensional array of 4 rows and seven columns to store the number of miles run by each runner each day.
• then implement the following functions:
  • a function to read and store the runners’ names and the numbers of miles run each day;
  • a function to find the total miles run by each runner and the average number of miles run each day

a function to output the results

A trucking company determined that the distance traveled per truck per year is normally​ distributed, with a mean of 50 thousand miles and a standard deviation of 10 thousand miles. Complete parts​ (a) through​ (b) below.

a. What proportion of trucks can be expected to travel between 37 and 50 thousand miles in a​ year?

The proportion of trucks that can be expected to travel between 37 and 50 thousand miles in a year is__.

​(Round to four decimal places as​ needed.)

b. What percentage of trucks can be expected to travel either less than 30 or more than 65 thousand miles in a​year?

The percentage of trucks that can be expected to travel either less than 30 or more than 65 thousand miles in a year is__.

​(Round to two decimal places as​ needed.)

c. How many miles will be traveled by at least 80​% of the​ trucks?

The number of miles that will be traveled by at least 80​% of the trucks is nothing miles.

​(Round to the nearest mile as​ needed.)

A trucking company determined that the distance traveled per truck per year is normally​ distributed, with a mean of 80 thousand miles and a standard deviation of 10 thousand miles. Complete parts​ (a) through​ (c) below. a. nbsp What proportion of trucks can be expected to travel between 66 and 80 thousand miles in a​ year? The proportion of trucks that can be expected to travel between 66 and 80 thousand miles in a year is . 4192. ​(Round to four decimal places as​ needed.) b. nbsp What percentage of trucks can be expected to travel either less than 55 or more than 95 thousand miles in a​ year? The percentage of trucks that can be expected to travel either less than 55 or more than 95 thousand miles in a year is 7.30​%. ​(Round to two decimal places as​ needed.) c. nbsp How many miles will be traveled by at least 85​% of the​ trucks? The amount of miles that will be traveled by at least 85​% of the trucks is nothing miles. ​(Round to the nearest mile as​ needed.)