A researcher conducts an experiment to examine the relationship between the weight gain of chickens whose diets had been supplemented by different amounts of amino acid lysine and the amount of lysine ingested. Since the percentage of lysine is known, and we can monitor the amount of feed consumed, we can determine the amount of lysine eaten. A random sample of 20 chickens was selected for the study. Data summarizing weight gains and amounts of lysine eaten over the test period are given here. (In the data, y represents weight gain in grams, and x represents the amount of lysine ingested in grams.)

x = c(0.1,0.26,0.371,0.234,0.137,0.086,0.251,0.085,0.188,0.187,0.265,0.183,0.359,0.168,0.293,0.269,0.357,0.347,0.172,0.229)

y = c(3.5,-4.5,-3.6,0.5,3.3,-4.8,0.2,7.0,4.4,-5.9,-1.4,2.0,3.3,4.4,4.9,5.4,-1.8,7.3,2.4,14.6)

Data set, lysine.csv, can be downloaded.

1. Obtain the estimated linear regression.

   x = 0.229 − 0.001y y = 2.84 − 0.063x y = 2.84 − 3.434x x = 0.229 − 0.063x

2. Find the standard errors for parameters.

   1.231 for intercept, and 0.235 for slope. 3.134 for intercept, and 12.872 for slope. 0.022 for intercept, and 0.004 for slope. 0.057 for intercept, and 0.235 for slope.

3. Conduct a hypothesis test for a linear relationship between weight gain and the amount of lysine eaten, and complete the test with significance level 0.01

   Since the test statistic is 0.906, there is no evidence to support the linear relationship. Since the test statistic is -0.267, there is no evidence to support the linear relationship. Since the test statistic is -0.267, there is evidence to support the linear relationship. Since the test statistic is 0.906, there is evidence to support the linear relationship.

4. Find 99% confidence interval for the expected weight gain when the amount of lysine eaten is 0.306

   [ -4.146 , 4.61 ] [ -2.589 , 6.167 ] [ 1.71 , 1.868 ] [ 0.153 , 0.311 ]

5. If the amount of lysine eaten by a chicken is 0.306 then the expected weight gain of chicken could be -2.1. Is this claim reasonable?

   The claim is reasonable in the linear regression. The claim is not reasonable in the linear regression. The claim is not validated by the linear regression.