COMM 291 ASSIGNMENT 6

COMM 291 ASSIGNMENT 6 - COMM 291 Application of Statistics...

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COMM 291 – Application of Statistics in Business (Jan–Apr 2010) ASSIGNMENT 6 – SOLUTIONS Question 1 a) Scatterplot and assumptions. All four assumptions are reasonable; the scatterplot shows an oval shape. Linearity – clear clustering around a straight line Constant variance – similar scatter around the regression line all along the x-axis Normality – no apparent skewness above or below the regression line Independence – the 25 websites were selected randomly! Students were asked to provide hand calculations and show their work in carrying out the regression. I have provided the Excel output to make it easy to check their results. SUMMARY’OUTPUT ’ Y’=’Design’Cost;’X’=’#’of’Pages Regression Statistics Multiple’R ’ 0.599’ R’Square ’ 0.359’ Adjusted’R’Sq ’ 0.331’ Standard’Error ’ 7705.626’ Observations’ 25’ ANOVA’ df SS MS F Significance F Regression’ 1’ 764851722.66’ 764851722.66’ 12.88’ 0.002’ Residual’ 23’ 1365663621.90’ 59376679.21’ Total’ 24’ 2130515344.56’ ’ ’ ’ ’ ’ ’ Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept’ 9701.33’ 6055.23’ 1.60’ 0.123’ -2824.86’ 22227.52’ No.’of’Pages ’ 1213.45’ 338.10’ 3.59’ 0.002’ 514.04’ 1912.85’
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b) Estimated regression equation: y ˆ = 9701.33 + 1213.45x The line is already plotted on the scatterplot above. c) H o : β 1 = 0 H a : β 1 0 F-stat = 12.88 OR t-stat = 3.59; either one gives a P-value of 0.002) There is strong evidence of linear relationship between design cost (y) and number of pages (x). d) 95% confidence interval for the marginal cost of an additional page on a new site. This question asks for a CI for the slope: From Excel output: (514.04 , 1912.85) By hand: t*(23 df) = 2.069 from the text and 2.068657 from Excel If you use 2.069 the CI is: 1213.45 ± 2.069(338.10) = 1213.45 ± 699.53 or (513.92 , 1912.98) The difference between the hand calculation and Excel is just due to round-off error.
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