A botanist conducted an experiment on the cold tolerance of the grass species Echinochloa crus--galli.

The CO2 uptake of 21 plants from Mississippi was measured at several levels of ambient CO2 concentration.

The variables are: Uptake and Concentration.

Call: lm(formula = Uptake ~ Concentration)

Coefficients:

	Estimate	Std. Error	T-value	Pr(>|t|)
(Intercept)	12.5418	1.3455		9.321E-08
Concentration	0.007523	0.0026		0.00848

A. T-statistic

Find the t-statistic for the test for the intercept ₀ : ₀ : ₀ = 0

Copy code and paste below with correct value (round to 4 decimals):

T_val_0 = # your answer here

print(T_val_0)

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# your code here

fail() # No Answer - remove if you provide an answer

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B. T statistic

Find the t-statistic for the test for the intercept ₁ : ₀ : ₁ = 0

Copy code and paste below with correct value (round to 4 decimals):

T_val_1 = # your answer here

print(T_val_1)

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# your code here

fail() # No Answer - remove if you provide an answer

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Analysis of Variance (ANOVA) Table

	Df	Sum Sq	Mean Sq	F value	Pr( >F)
Regression	___	102.84	___	___	___
Errors	___	226.67	___
Total	___	___

C. ANOVA table missing values

Fill in the missing values in the ANOVA table above. We are going to do that by filling in the values in the code bellow:

Copy the following code and enter it in the following cell. Prodide the corresponding values

df.regression= #degrees of freedom for SS Regression

df.residuals = #degrees of freedom for SS Residuals (errors)

df.total = #degrees of freedom for SS Total

SST= # Sums of squares Total

MSR= # Mean Sum os squares for Regression

MSE= # Mean Sum os squares Errors

F= # F statistic

pval= # p-value for the F-test

results<-c(df.regression,df.residuals,df.total,SST,MSR,MSE,F,pval)

results

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# your code here

fail() # No Answer - remove if you provide an answer

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D. Find Residual Standard Error:

Copy code and paste below with correct value (round to 5 decimals):

res.sd= # your answer

res.sd # this line is so that you see the value

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# your code here

fail() # No Answer - remove if you provide an answer

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E. Coefficient of Determination

Find R-squared:

Copy code and paste below with correct value (round to 4 decimals):

Rsq= # value of R-squared

Rsq # this line is so that you see the value

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# your code here

fail() # No Answer - remove if you provide an answer

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F. Sigma

Obtain a point estimate for ²

Copy code and paste below with correct value (round to 2 decimals):

Sigmasq= # your answer

Sigmasq # this line is so that you see the value

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# your code here

fail() # No Answer - remove if you provide an answer

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G. Confidence Interval for the Slope

Find the 95% confidence interval for the slope.

Copy code and paste below with correct value (round to 5 decimals):

slope.lower= # lower bound for the slope ₁

slope.upper= # upper bound for the slope ₁

c(slope.lower,slope.upper) # this line is so that you see the value

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# your code here

fail() # No Answer - remove if you provide an answer

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H. Confidence Interval for mean response

Find a confidence interval for the mean response at when the ambient CO2 concentration is 340.

You can use that mean ambient CO2 concentration is 435 and _xx = 7180829

Copy code and paste below with correct value (round to 5 decimals):

fitted= # fitted value for C02 = 340

tval= # critical value for the t distribution with corresponding degrees of freedom

mean.se= # standard error for mean response

meanresp.lower= # lower bound for the mean response

meanresp.upper= # upper bound for the mean response

c(fitted,meanresp.lower ,meanresp.upper) # this line is so that you see the value

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# your code here

fail() # No Answer - remove if you provide an answer

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