The article The Influence of Temperature and Sunshine on the Alpha-Acid Contents
ID: 3310553 • Letter: T
Question
The article The Influence of Temperature and Sunshine on the Alpha-Acid Contents of Hopst reports the folowing data on yield (y), mean temperature over the period between date of coming into hops and date of picking (x), and mean percentage of sunshine during the same period (x2) for the Fuggle variety of hop: 16.7 17.4 18.4 16.8 18.9 17.1 17.3 18.2 21.3 21.2 20.7 18.5 0 42 47474341 48 44 43506 60 2101101031039176737068534531 Use the following R Code to complete the regression analysis x1- c(16.7,17.4,18.4,16.8,18.9,17.1,17.3,18.2,21.3,21.2,20.7,18.5) x2- c(30,42,47,4743,41,48,44,43,50,56,60) y c(210,110,103,103,91,76,73,70,68,53,45,31) mod im(ywx1+x2) summary(mod) (a)According to the output, what is the least squares regression equation y . bo++bzx2: (Round each value to 3 dedmal places.) (b) What is the estimate for …[ CHint: This is referred to as the residual standard error in R output) (c) According to the model what is the predicted value for decimal places) when x1-17.3 and x2 . 48 and what is the responding residual? (Round your answers to four Residual (d) Test Ho: .-P2-oversus H., either 1 or B2 * 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 p-value » State the concluion in the problem context There is moderately Suggestive evidence at least one of te explanatory variables isa significant predictor of the response. There is convincing evidence at least one of the explanatory variables is a significant predictor of tho response. 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. when xi-17.3.nd K-4Biss.10.13. use this to obtain the 95% a forPr.173, 48, (Round your answers to (e) The estimated standard deviation of two decimal places) (r) use the information in parts (b) and (e) to obtain a95% Pl for yield in a Mure experiment when x.-17.3 and x2 . 48. (Round your answers to two decimal places (9)Given that x is in the model, would you retain x? 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 in the Appendix of Tables to answer this question.Explanation / Answer
Output :
> x1=c(16.7,17.4,18.4,16.8,18.9,17.1,17.3,18.2,21.3,21.2,20.7,18.5)
> 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=lm(y~x1+x2)
> summary(mod)
Call:
lm(formula = y ~ x1 + x2)
Residuals:
Min 1Q Median 3Q Max
-41.730 -12.174 0.791 12.374 40.093
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 415.113 82.517 5.031 0.000709 ***
x1 -6.593 4.859 -1.357 0.207913
x2 -4.504 1.071 -4.204 0.002292 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 24.45 on 9 degrees of freedom
Multiple R-squared: 0.768, Adjusted R-squared: 0.7164
F-statistic: 14.9 on 2 and 9 DF, p-value: 0.001395
a)The regression equation :
y = 415.113 – 6.593*x1 – 4.504*x2
b) s = 24.45
c) When x1 = 17.3 and x2 = 48, predicted y = 84.8621.
Residual = 73 – 84.8621 = -11.8621.
d) F-statistic: 14.9 on 2 and 9 DF, p-value: 0.001395.
There is convincing evidence at least one of the explanatory variables is a significant predictor of the response.
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