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)
predict(mod,data.frame(x1=21.3,x2=43),interval="confidence")
predict(mod,data.frame(x1=21.3,x2=43),interval="prediction")
> 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 > > predict(mod,data.frame(x1=21.3,x2=43),interval="confidence") fit lwr upr 1 81.03364 43.52379 118.5435 > predict(mod,data.frame(x1=21.3,x2=43),interval="prediction") fit lwr upr 1 81.03364 14.19586 147.8714
a)
y^ = 415.113 -6.593 x1 -4.504 x2
b)
24.45
c)
y^ = 81.0336
residual = yi - y^
= 68 - 81.0336
= -13.0336
d)
F = 14.9
p-value = 0.0014
conclusion
option D) convincing evidence
e)
(43.52,118.54)
f)
(14.2,147.87)
The article "The Influence of Temperature and Sunshine on the Alpha-Acid Contents of Hops"t reports the followi...
The article The Influence of Temperature and Sunshine on the Alpha-Acid Contents of Hops t reports the following data on yield (y), mean temperature over the period between date of coming into hops and date of picking (x1), and mean percentage of sunshine during the same period (x2) for the Fuggle variety of hop 16.7 17.418.4 16.8 18.9 17.1 17.3 18.2 21.3 21.2 20.7 18.5 30 42 47 47 43 48 43 50 56 60 41 210 110 103 103...
Please explain steps and solve thanks The article "The Influence of Temperature and Sunshine on the Alpha-Acid Contents of Hops"t reports the following data yield (y), mean temperature over the period between date of coming into hops and date of picking (x1), and mean percentage of sunshine during the same period (x2) for the Fuggle variety of hop: 21.3 X1 16.7 17.4 18.4 16.8 18.9 17.1 17.3 18.2 21.2 20.7 18.5 30 47 43 48 50 56 60 X2 42...
The ability of ecologists to identify regions of greatest species richness could have an impact on the preservation of genetic diversity, a major objective of the World Conservation Strategy. A study used a sample of n = 31 lakes to obtain the estimated regression equation y 3.89 0.033x1 +0.024x2 0.023x3 0.0080x4 - 0.13x5 0.72x6 where y species richness, x1 = watershed area, x2 = shore width, x3 = poor drainage (%), x4 = water color (total color units), x5 sand...
Consider a binary response variable y and two explanatory variables x1 and x2. The following table contains the parameter estimates of the linear probability model (LPM) and the logit model, with the associated p-values shown in parentheses. Variable LPM Logit Constant −0.60 −2.50 0.02 (0.03 ) x1 0.28 0.99 (0.06 ) (0.06 ) x2 −0.06 −0.30 (0.03 ) (0.06 ) a. At the 5% significance level, comment on the significance of the variables for both models. Variable LPM Logit x1...
Consider a binary response variable y and two explanatory variables xy and x2. The following table contains the parameter estimates of the linear probability model (LPM) and the logit model, with the associated p-values shown in parentheses. Constant .40 -2.30 x1 x2 0.06 (0.03) 0.36 0.90 (0.03)(0.07) -0.03-0.10 (0.02) (0.01) a. At the 5% significance level, comment on the significance of the variables for both models. Logit gnificant 0 (Not significant x1 x2 b. What is the predicted probability implied...
Use the Minitab output to answer the following questions. 1. What is the estimated value of B2? 2. What is the value of SST? 3. What is the value of MSR? 4. What is the value of S2? 5. What is the predicted value of Y when X1 = 7, X2 = 5, and X3 = 3? (round your answer to two decimal places) 6. What is the residual for the predicted value in question 5? The value of Y...
A regression analysis is performed using data for 36 single-family homes to predict appraised value (in thousands of dollars) based on land area of the property (in acres), X1i, and age (in years), X2i, in month i. Use the results below to complete parts (a) and (b) below. Variable Coefficient Standard Error t Statistic p-value Intercept 392.60372 51.68272 7.60 0.0000 Area, X1 451.43475 100.48497 4.49 0.0001 Age,X2 −2.17162 0.79077 −2.75 0.0097 a. Construct a 95% confidence interval estimate...
Use the following linear regression equation to answer the questions. x1 = 1.5 + 3.4x2 – 8.3x3 + 2.3x4 (a) Which variable is the response variable? Which variables are the explanatory variables? (b) Which number is the constant term? List the coefficients with their corresponding explanatory variables. constant? x2 coefficient? x3 coefficient? x4 coefficient? (c) If x2 = 1, x3 = 8, and x4 = 6, what is the predicted value for x1? (Use 1 decimal place.) (d) Explain how...
QUESTION 27 Q27. A manager at a local bank analyzed the relationship between monthly salary (y, in $) and length of service (x, measured in months) for 30 employees. She estimates the model: Salary = Bo + B1 Service + ε. The following ANOVA table below shows a portion of the regression results. df SS M S F Regression 555,420 555,420 7.64 Residual 27 1,962,873 72,699 Total 28 2 ,518,293 Coefficients Standard Error t-stat p-value Intercept 784.92 322.25 2.44 0.02...
Consider the following set of dependent and independent variables. Complete parts a through c below. y 10 11 14 14 20 24 26 32 저15597121521 x2 17 11 13 11 2 8 6 4 a. Using technology, construct a regression model using both independent variables. y = 1 3.5734 ) + ( 0.9496 ) x 1 + (-0.4001 ) x2 (Round to four decimal places as needed.) b. Test the significance of each independent variable using a 0.10. Test the...