Each box of Healthy Crunch breakfast cereal contains a coupon entitling you to a

Question

Each box of Healthy Crunch breakfast cereal contains a coupon entitling you to a free package of garden seeds. At the Healthy Crunch home office, the weight of incoming mail is used to determine how many of their employees are to be assigned to collecting coupons and mailing out seed packages on a given day. (Healthy Crunch has a policy of answering all its mail on the day it is received.) Let x = weight of incoming mail and y = number of employees required to process the mail in one working day. A random sample of 8 days gave the following data. x (lb) 10 21 14 6 12 18 23 25 y (Number of employees) 7 12 7 5 8 14 13 16 x = 129, y = 82, x2 = 2395, y2 = 952, and xy = 1497 (a) Draw a scatter diagram for the data. Submission Data Correct: Your answer is correct. (b) Find x, y, b, and the equation of the least-squares line. (Round your answers to three decimal places.) x = y = b = y = + x Plot the line on the scatter diagram of part (a). WebAssign Plot WebAssign Plot WebAssign Plot WebAssign Plot Correct: Your answer is correct. (c) Find the sample correlation coefficient r and the coefficient of determination r2. (Round your answers to three decimal places.) r = r2 = What percentage of variation in y is explained by the least-squares model? (Round your answer to one decimal place.) % (d) If Healthy Crunch receives 16 pounds of mail, how many employees should be assigned mail duty that day? (Round your answer to the nearest whole number.) employees

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: Y
Independent Variable: X
Y = 1.3009131 + 0.55498214 X
Sample size: 8
R (correlation coefficient) = 0.93263275
R-sq = 0.86980384
Estimate of error standard deviation: 1.5554673

Parameter estimates:

Analysis of variance table for regression model:

Predicted values:

Hence,

b) y = 1.301 + 0.555 X

c) r = 0.933

r2 = 0.870

87.0% of the variation in y is explained by the least square model.

d) For x = 16, y = 10.18

Hence,

10 employees should be assigned mail duty that day.

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 1.3009131 1.5166996 0 6 0.85772625 0.424 Slope 0.55498214 0.08765805 0 6 6.331217 0.0007

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