(Assume you have noted the following prices for paperback books and the number o
ID: 3157754 • Letter: #
Question
(Assume you have noted the following prices for paperback books and the number of pages that each book contains. Book Pages (X) Price (Y) A 500 $7.00 B 700 7.50 C 750 9.00 D 590 6.50 E 540 7.50 F 650 7.00 G 480 4.50 H 380 $3.50 (H got a little messed up, but 380 is under x and $3.50 is under y) a. Develop a least-squares estimated regression line. b. compute the coefficient of determination and explain its meaning. c. compute the correlation coefficient between the price and the number of pages d. compute the correlaion coefficient e. use the t test to determine whether the slope of the regresssion model is significant at a= 0.1
Explanation / Answer
Let independent variable X = Book pages
dependent variable Y = Price
There are 9 data pairs.
We can done all these questions using Regression.
Regression using MINITAB :
STAT --> Regression --> Regression --> Response : y --> Predictors : x --> Results : select second option --> ok --> ok
a. Develop a least-squares estimated regression line
The regression equation is
y = - 0.49 + 0.0123 x
b. compute the coefficient of determination and explain its meaning.
Coefficient of determination = Rsq = 73.8%
It exrpesses the proportion of variation in price which is explained by variation in book pages.
c. compute the correlation coefficient between the price and the number of pages
Correlation coefficient (r) = =sqrt(Rsq) = sqrt(73.8%) = 0.8591
The correlation coefficient between price and book pages is 0.8591.
e. use the t test to determine whether the slope of the regresssion model is significant at a= 0.1
Here the hypothesis for the test is,
H0 : B = 0 Vs H1 : B not= 0
B is population slope for book pages.
Predictor Coef SE Coef T P
Constant -0.492 1.751 -0.28 0.788
x 0.012295 0.002993 4.11 0.006
S = 0.974399 R-Sq = 73.8% R-Sq(adj) = 69.4%
The test statistic is t = 4.11
P-value = 0.006
P-value < a (0.1)
Reject H0 at 10% level of significance.
The result is significant.
Conclusion : Population slope for book pages is differ than 0.
That is we can conclude the variable book pages.
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