Can the age of a cow be used to predict its milk production? The ages of...

Can the age of a cow be used to predict its milk production? The ages of eight cows (in years) and their milk production (in gallons per week) are shown below: Age 4 4 6 7 7 8 10 11 Milk Production 37.0 35.4 33.3 35.6 32.3 33.7 32.1 29.6 A regression analysis is conducted and the equation of the least squares regression line is found to be ^y = 39:297 - 0:796x. It is also determined that 73.2% of the variation in milk production can be accounted for by age. We also calculate P P (yi - y^i)2 = 7:90 and (xi - x)2 = 44:9.

What is the sample correlation between age and milk production?

A 90% condence interval for the parameter 1 in the linear regression model is?

We conduct a hypothesis test of H0: 1 = 0 vs. Ha: 1 < 0 to determine whether there exists a negative linear relationship between the age of a cow and its milk production. The P-value for the appropriate test of signicance is?

Expert Solution

(a) r = √0.732 = 0.856

Since the correlation is negative (as seen from the scatter plot), r = -0.856

(b) The 905 confidence interval for the intercept term is [36.4306, 42.1639]

(c) p- value for a lower tailed test with t = -4.052 and df = 6 is 0.0034

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orchestra answered 2 years ago

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