3. Find the correlation and regression lines for the data above.

r=

LinReg(ax+b)=

Based on the data below, forecast US hotel revenues for 2017, 2018, and 2019. Provide the model developed for your calculations.

YEAR REVENUE ($USD BILLION)

2001 105.00

2002 111.90

2003 118.80

2004 119.30

2005 135.50

2006 146.20

2007 153.80

2008 154.70

2009 133.30

2010 142.00

2011 153.30

2012 155.50

2013 163.00

2014 176.70

2015 189.50

2016 199.30

1. Define the term skewness and kurtosis. With the aid of a diagram, describe the three types of kurtosis.            4marks
2. Describe the components of a time series and mention their applicability. 4marks

3. The table below relates to the sales of refrigerators by a certain firm in Kenya.

Year production in (000) Year Production in (000)

1996 17    2002 35

1997 20 2003   55

1998 19 2004 50

1999 26 2005 74

2000 24 2006 69

2001 40

Using this data;

1. Fit a straight line trend by the method of ordinary least squares
2. ii. Estimate the number of refrigerators that will be sold in the year 2009.

On October 17, 2007, the classified ads on the web site of The Seattle Times listed the following 13 used Toyota Prius automobiles for sale; the data set below shows the year, color, mileage (in miles) and asking price (in U.S. dollars) for each car:

year     color      mileage     price
2006     green        17043     25995
2007     gray         12628     24980
2005     maroon       24039     24885
2005     silver       48226     23995
2006     black        10522     22995
2004     silver       66345     21995
2007     white         5611     21995
2005     gold         24479     21595
2004     white        14618     20995
2005     silver       53699     20980
2004     silver       47649     17995
2003     white        39600     17500
2005     black       103126     16995

We wish to investigate a possible association between the mileageof each Prius and its price. You should construct a scatterplot of this data.

assume that a linear model is appropriate, regardless of your answer to the previous question.

1. Find the equation of the regression line for this data that predicts price based upon mileage:

2. Use the model to predict the asking price of a Toyota Prius with 450,000 miles, or explain why such a prediction is not appropriate:

3. Use the model to predict the asking price of a Toyota Prius with 45,000 miles, or explain why such a prediction is not appropriate:

4. Compute the residual for the green Prius:

1. The table below gives the annual total returns on Global Balanced Index Fund from 1999 to 2008. The returns are in the local currency. Use the information in this table to answer the following questions:

a. Calculate the mean absolute deviation (MAD).

2. Calculate the variance.

3. Calculate the standard deviation.

d. Calculate the semi variance (the average squared deviation below the mean), a measure of downward risk.

You will receive $2,000 on January 1st 2004, on January 1st in 2005 and January 1st 2006. Which of the following expressions will calculate your value at time of January 1st 2004?

a

PV = $2,000​[1.06]^-1 + $2,000​[1.06]^-2 + $2,000​[1.06]^-3

b

PV = $2,000​[1.06]^1 + $2,000​[1.06]^2 + $2,000​[1.06]^3

c

PV = $2,000​[1.06]^0 + $2,000​[1.06]^1 + $2,000​[1.06]^2

d

PV = $2,000 + $2,000​[1.06]^-1 + $2,000​[1.06]^-2

The table below gives the annual total returns on Global Balanced Index Fund from 1999 to 2008. The returns are in the local currency. Use the information in this table to answer the following questions:

1. (5.0 pts) Calculate the mean absolute deviation (MAD).

2. (4.0 pts) Calculate the variance.

Solution

3. (2.0 pts) Calculate the standard deviation.

Solution

3. (4.0 pts) Calculate the semi variance (the average squared deviation below the mean), a measure of downward risk.

Solution:

Question 4 Using the dataset below, estimate whether there is a difference among the graduation rates - identified as percentages - of five high schools over a 10-year period. Explain your results. Yr HS 1 HS 2 HS 3 HS 4 HS 5 2003 67 82 94 65 88 2004 68 87 78 65 87 2005 65 83 81 45 86 2006 68 73 76 57 88 2007 67 77 75 68 89 2008 71 74 81 76 87 2009 78 76 79 77 81 2010 76 78 89 72 78 2011 72 76 76 69 89 2012 77 86 77 58 87

The following table shows the number of customer complaints against airlines operating in a country during the given year.

Use interpolation to estimate the number of complaints in 2005.

(Round your answer to the nearest whole number.)

The interpolated value for

2005 is _______ complaints.