Problem 4 In order to investigate the feasibility of starting a Sunday edition f
ID: 3317435 • Letter: P
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Problem 4 In order to investigate the feasibility of starting a Sunday edition for a large metropolitan newspaper, information was obtained from a sample of newspapers concerning their Daily and Sunday circulations (both in thou- sands). In the Minitab output below Daily denotes daily circulation and Sunday, a response variable, denotes Sunday circulation. a) Is there a statistically significand linear relationship between Daily and Sunday? Test at = 0.05. (State the hypothesis test, rejection rule and your conclusion. b) Interpret coefficients in the regression model of Sunday on Daily. c) Compute the r for this regression and interpret it. What is the correlation coefficient between Daily and Sunday? d) A consultant claims that for a 10,000 increase in Daily circulation, Sunday circulation would increase by 15,000 thousand. Does the estimated model validate her claim? To answer the question construct an appropriate 95% confidence interval. e) A consultant also claims that expected Sunday circulation for news- papers with daily circulation of 400,000.is 500,000. Is the consultant correct. Answer by constructing an appropriate 95% confidence interval. f) Now suppose that a regression model was estimated with Daily cir- culation as a dependent variable and Sunday circulation as an independent variable. Find the missing coefficient of Sunday circulation. What is the r2 of this new regression?Explanation / Answer
a. As we can see from the first table that the p-value of the test whether regression coefficient is significant or not, is .381 which is greater than desirable alpha value.i.e. .05 So we accept the null hypothesis i.e regression coefficient is not significant.
b As the regression equation is sunday =30.7+1.32Daily
that implies for one unit change in Daily sunday will increase by 1.32 units
c. the R2 is given by R2=(sum of square due to regressors)/(total sum of square)
[Sum of squares are not given in the question]
d. To know how much Sunday circulation will vary for varying daily circulation we need to have the estimated range of the regression coefficient(with 95% confidence,as per the question).By multiplying the regression coefficient by 15000 we will get the varying range of Sunday circulation.
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