Discuss the below:
Project Quantitative methods
Q1. In testing 9 sedans, Cars and Driver magazine rated each on 13 different characteristics, including ride, handling, and driver comfort. Each vehicle also received an overall rating. Scores for each vehicle were as follows;
Y= x3=
Car Overall x1 = x2 = Driver
Rating Ride Handling Comfort
1 83 8 7 7
2 86 8 8 8
3 83 6 8 7
4 83 8 7 9
5 95 9 9 9
6 84 8 8 9
7 88 9 6 9
8 82 7 8 7
9 92 8 9 8
a. Determine the least-squares multiple regression equation.
b. Interpret the y-intercept and partial regression coefficients.
c. What is the estimated overall rating for a vehicle that scores 6 on ride, 9 on handling, and 7 on driver comfort?
Q2. Fit a linear trend equation to the following data describing average hourly earnings of U.S. production workers. What is the trend estimate for 2010?
Years: 2001 2002 2003 2004
Average hourly
Earnings: $14.53 $14.95 $15.35 $15.67
Q3. From 1997 through 2004, the value of U.S. exports to Mexico was as shown below. Data are in billions of dollars.
Year 1997 1998 1999 2000
Export: $71.4 $78.8 $86.9 $111.3
Year: 2001 2002 2003 2004
Export: $101.3 $97.5 $97.4 110.8
a. Fit a linear trend equation to the time series. Using this equation, determine the trend estimate for 2012.
b. Fit a quadratic equation to the time series, then use the equation, determine the trend estimate for 2012.
c. Construct a graph of the time series along with the equations fitted in parts (a) and (b). Which equation appears to better fit the data.
Q4 The following data show residential and commercial natural gas consumption (quadrillion Btu) from 1985 through 2000.
Year Consumption Year Consumption
1985 27.6 1993 30.6
1986 26.9 1994 30.8
1987 27.6 1995 31.6
1988 28.9 1996 33.0
1989 29.4 1997 33.0
1990 29.2 1998 32.8
1991 30.1 1999 35.8
1992 29.6 2000 37.4
a. Construct a graph of the time series, then superimpose a three-year centered moving average over the original series.
b. Superimpose a five-year centered moving average over the original series. Why is the moving average "smoother" when N=5?.
Q5 U.S. cellular phone subscribership has reported as shown below fro 1993- 2004 period.
Year Subscribers Year Subscribers
(Millions) (Millions)
1993 16.0 1999 86.0
1994 24.1 2000 109.5
1995 33.8 2001 128.4
1996 44.0 2002 140.8
1997 55.3 2003 158.7
1998 69.2 2004 182.1
From the data, use the weighting constant α = 0.5 and exponential smoothing to determine the forecast for 2005.
Q6. When the robot welder is functioning properly, the natural gas cylinders being produced have average burst strength of 3400 psi, with a standard deviation of 100 psi. Determine the centerline and the upper and lower control limits for a 3-sigma mean control chart in which each sample consists of 4 cylinders.
Q7. Automobiles are randomly selected for a clase examination for fit-and-finish defects, including such items as dirt specks in the paint and panels that are not properly aligned. Based on data collected for the following vehicles that were so inspected, construct a 3-sigma c-chart, then reach a conclusion regarding whether the process is in control.
Vehicle c=Number Vehicle c=Number
Number of Defects Number of Defects
1 4 11 6
2 7 12 10
3 4 13 5
4 9 14 10
5 9 15 7
6 8 16 6
7 7 17 8
8 6 18 5
9 7 19 7
10 5 20 11