Question
This Was the R output
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
My Notes OAsk Your Teach 6. o 3.58 points 1/4 Submissions Used yield (Y), mean temperature over the period ing into hops and date o X1), and mean percentage o ring the same period (X2) for the Fuggle variety of hop X1 16.7 17.4 18.4 16.8 18.90 17.1 17.3 18.2 21.3 21.2 20.7 18.5 X2 30 42 47 43 41 48 44 43 50 56 60 210 110 103 103 76 73 70 68 53 45 Use the following R Code to complete the regression analysis: 20.7,18.5) x2 c 45,31) mod summary(mod) (a)According to the output, what is the least squares regression equation bo+b1x1+b2x2: (Round each value to 3 decimal places. 415.113 -6.593 X1 504 X2 (b) What is the estimate for a? s 4.45 (Hint: This is referred to as the residual standard error in R output) (c) According to the model what is the predicted value for when x1 17.1 and x2 41 and what is the corresponding residual? (Round your answers to four decimal places.) 17.7087 Residual: y (d) Test Ho: B1 32 0 versus Ha: either B1 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.) f 4.26 p-value 4.90 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 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. There is slightly suggestive evidence at least one of the explanatory variables is a significant predictor of the response. (e) The estimated standard deviation of when X1 17.1 and X2 41 is s. 9.76 Use this to obtain the 95% CI for ay 17.1, 41. (Round your answers to two decimal places.) (f) Use the information in parts (b) and (e) to obtain a 95% PI for yield in a future experiment when x1 17.1 and x2 41. Round your answers to two decimal places.
Explanation / Answer
d) F= 14.9
p-value= 0.001395
Since p-value < 0.05, so at 5% level of significance, we can conclude that there is convincing evidence that atleast one of the explanatory varaible is a significant predictor of the response.
