The article \"The Influence of Temperature and Sunshine on the Alpha-Acid Conten

Question

The article "The Influence of Temperature and Sunshine on the Alpha-Acid Contents of Hops" reports the following data on yield (y), mean temperature over the period between date of coming into hops and date of picking (x_1). and mean percentage of during the same period (x_2) for the Fuggle variety of hop: Use the following R Code to complete the regression analysis: x1 = c(16, 7, 17, 4, 18, 4, 16, 18, 9, 17.1, 17.3, 18.2, 21.3, 21.2, 20.7, 18.5) x2 = c(30, 42, 47, 47, 43, 41, 48, 44, 43, 50, 56, 60) y = c(210, 110, 103, 103, 91, 76, 73, 70, 68, 53, 45, 31) mod = Im(y ~ x1 + x2) summary(mod) According to the output, what is the least squares regression equation y = b_0 + b_1 x_1 + b_2 x_2:(Round each value to 3 decimal places.) What is the estimate for sigma? According to the model what is the predicted value for y when x_1 = 17.1 and x_2 = 41 and what is the corresponding residual? (Round your answers to four decimal places.). Test H_0: beta_1 = beta_2 = 0 versus H_a: either beta_1 or beta_2 notequalto 0 From the output state the test statistic and the p-value. Round your test stat to one decimal place and your p-value to 4 decimal places.) State the conclusion in the problem context. There is no suggestive evidence at least one of the explanatory variables is a significant predictor of the response. There is slightly suggestive evidence at least one of the explanatory variables is a significant predictor of the response. There is moderately suggestive evidence at least one of the explanatory variables is a significant predictor of the response. There is convincing evidence at least one of the explanatory variables is a significant predictor of the response. The estimated standard deviation of y when x_1 = 17.1 and x_2 = 41 is = 9.76. Use this to obtain the 95% CI for y 17.1, 41. (Round your answers to two decimal places.) Use the information in parts (b) and (c) to obtain a 95% PI for yield in a future experiment when x_1 = 17.1 and x_2 = 41. (Round your answers to two decimal place.) Given that x_2 is in the model, would you retain x_1? Yes, there is evidence this factor is significant. It should remain in the model. No, there isn't evidence this factor is significant. It should be dropped from the model. You may need to use the appropriate table m the Appendix of Tables to answer this question.

Explanation / Answer

A-Regression equation is

Y=415.113-6.593x1-4.504x2

B-Sigma=24.45

C-Y_hat=415.113-6.593*17.1-4.504*41 =117.7087

Residual =y-Y_hat = 76-117.7087 =-41.7087

D- F-statistic =14.9

p-value=0.001395=0.0014

Conclusion-Last option

E-Confidence interval=( 95.66 139.80)

Using following commands

predict(mod, interval="confidence", level=0.95)

F-Prediction interval=(58.17   177.29)

Using following commands

predict(mod, interval="prediction", level=0.95)

G-No, because x1 is not a significant predictor of Y.

Second option is answer.

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