Question

In: Statistics and Probability

1. Use the data below to find the linear regression equation that best represents the given...

1. Use the data below to find the linear regression equation that best represents the given data and predict the revenue in 2013 (Copy data to Excel)

2. Then create Two new columns that represent the predication y =mx+b for each year and percent of growth for each year = (Revenue/Predication)*100

3. Use Excel to graph the linear model (x-axis years, y-axis revenue) and the linear equation of best fit.

Year Revenue Predication Percent of growth (%)
2001 3665
2002 4163
2003 4750
2004 5287
2005 5825
2006 6395
2007 6834
2008 6994
2009 7401
2010 7867
2011 8548
2012 9331
  1. Fill out the missing entry for prediction and percent of growth
  2. Find the value of the linear correlation coefficient r.
  3. Find the equation of the regression line, letting Number of years be the independent (x) variable.
  4. Find the coefficient of determination.
  5. Find the standard error of estimate se.
  6. Report the result in APA format
  7. Show work in Excel if possible

Solutions

Expert Solution

Solution :-

Given data,

1) Process: data -> data analysis -> regression -> dependent variable = revenue ; independent variable = t

Output:

regression equation: revenue = 3282.438 + 482.958*t

for t = 13;      
predicted revenue =   =3282.438 + 482.958*13 =   9560.892

2)

Year t Revenue Predication; yhat = 3282.438 + 482.958*t Percent of growth (%) = (Revenue/Predication)*100
2001 1 3665 3765.397436 0.973336829
2002 2 4163 4248.355478 0.979908584
2003 3 4750 4731.31352 1.003949533
2004 4 5287 5214.271562 1.013947958
2005 5 5825 5697.229604 1.022426759
2006 6 6395 6180.187646 1.034758225
2007 7 6834 6663.145688 1.025641689
2008 8 6994 7146.10373 0.978715152
2009 9 7401 7629.061772 0.970106184
2010 10 7867 8112.019814 0.969795462
2011 11 8548 8594.977855 0.994534267
2012 12 9331 9077.935897 1.027876833

3)

4)

a) correlation coefficient = 0.995294997   [Excel function used CORREL(t,revenue)]
  
b) regresion line: y = 482.96x - 962634   [from the column of coefficients in regression output]
  
c) coefficient of determination, R^2 = r^2 = 0.995295^2 =    0.990612137
  
d) SE = 177.7907239   [ deom standard error in table 1]


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