The marketing unit at your firm has collected data for the past 20 questers on a
ID: 3218999 • Letter: T
Question
The marketing unit at your firm has collected data for the past 20 questers on a specific product that your team manufactures. The data shows how two entities have rated your product over time-a quality index value calculated by an industry group and another a customer rating by a customer group. The table below shows the index values and customer ratings for these 20 quarters. Determine the values of the parameters a and b in the linear regression equation using the least squares method. Write the linear regression equation for this data. Determine the coefficient of correlation r of this data. What can you say about the strength of the prediction over the range and the relationship between these two measures of quality? What percentage of variability is accounted for by the relationship between the two variables and what does this statistic mean? Using the relationship in part (a) what would you predict the customer measure to be if you knew the quality index value was 2Explanation / Answer
Sol:
take X independent variable as quality index
and Y as customer rating
used excel to get regression eq
reg eq is
customer rating=0.627+0.028(quality index)
a=y inetrcept=0.627
b=slope=0.028
Solutionb:
correaltion coefficient =r
r=0.524
there exists a positive relationship between quality index and customer rating
that is
as quality index increases customer rating increases.
Solutionc:
from output R sq=0.274
R sq=coefficient of determination
27.4% variation in customer rating is explained by regression model
Rest 100-27.4=72.6% remains unexplained
SOlutiond:
for X=26 what is y
substitute in Reg equation is
Y=0.627+0.028(X)
customer rating=0.627+0.028(26)
=1.355
=1.4(rounding to 2 decimals)
SUMMARY OUTPUT Regression Statistics Multiple R 0.524128 R Square 0.27471 Adjusted R Square 0.234416 Standard Error 0.559251 Observations 20 ANOVA df SS MS F Significance F Regression 1 2.132297 2.132297 6.817651 0.017683 Residual 18 5.629703 0.312761 Total 19 7.762 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Intercept 0.627119 0.890792 0.704002 0.49044 -1.24437 2.498603 -1.24437 quality index 0.028431 0.010889 2.611063 0.017683 0.005555 0.051307 0.005555Related Questions
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