“Problem 2. Ziba, Inc. has provided the following information regarding one of their products for the years 1986 through 2010.
1. Sales in $1,000,000 (Y)
2. Advertising in $1,000 (X1)
3. Price in $100 (X2)
4. Competitor’s Price in $100 (X3)
5. Time (X4),
where 1986 = 1. The data file “Regression and Correlation Data-V10” is located in Assessment 6 folder. Refer to that data file and perform the following analyses and fully explain your results.
a. Run a correlation analysis and explain your results. Be sure to discuss the concept of multicollinearity.
b. Run a regression analysis relating sales (Y) and all of the independent variables [Advertising (X1) through Time (X4).] Is the regression model significant? Explain how you arrived at your answer.
c. Which variables are significant and which are not? Explain how you arrived at your answer.
d. Drop the variable(s) that at 95% confidence were not significant in part “b” and run a new regression analysis. Write your estimated regression equation.
e. What is the value of R-square you found in part “d”?
Fully explain the meaning of the R-square that you found.
f. Use the model of part “d” and forecast sales for 2011 through 2013, assuming the company is planning to increase the price by 4% annually in years 2011 through 2013.
Show your computations and write your answers below.
Year Your Sales forecasts 2011 2012 2013
Year Sales (Y) Advertising (X1) Price (X2)
Competitor’s Price (X3) Time (X4) 1986 1578 400 21.00 20 1 1987 1678 580 21.19 22 2 1988 1800 678 23.10 19 3 1989 1850 776 23.30 21 4 1990 1900 874 25.40 21 5 1991 1950 972 25.63 21 6 1992 2000 1070 27.94 20 7 1993 2050 1168 28.19 22 8 1994 2100 1220 30.72 24 9 1995 2456 1272 31.00 18 10 1996 2812 1324 33.79 21 11 1997 3168 1376 34.10 23 12 1998 3524 1379 37.16 23 13 1999 3880 1382 37.50 17 14 2000 3900 1385 40.87 18 15 2001 3920 1388 41.24 16 16 2002 3940 1391 44.95 25 17 2003 3960 1399 45.36 26 18 2004 3980 1407 49.44 28 19 2005 4000 1415 49.88 18 20 2006 4020 1423 54.37 24 21 2007 4040 1460 54.86 23 22 2008 4060 1497 59.80 24 23 2009 4080 1534 60.34 21 24 2010 4100 1571 65.77 23 25”
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