Show your work and clearly explain each step (and your answer). You may only use

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Show your work and clearly explain each step (and your answer).

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4. QUESTION 4 20 pts The number of calories and number of grams of sugar per serving were measured for 36 breakfast cereals. Consider the following linear regression output ## Call: ## lm(formula = Calories " Sugar) ## Residuals: ##-37.428-9.832 0.245 8.909 40.322 ## Coefficients Min 1Q Median 3Q Max ##(Intercept) 87.4277 ## Sugar Estimate Std. Error t value Pr(>Itl 5.1627 16.935

Explanation / Answer

SolutionA:

From Regression output:

calories=87.4277+2.4808(sugar)

Given x=10 grams of sugar

substitute in regression eq

calories=87.4277+2.4808(10)

= 112.2357

Solutionb:

Residual=actual value-predicted value

actual value=110 calores

predicted value can be calculated from

calories=87.4277+2.4808(grams)

=87.4277+2.4808(1)

= 89.9085

Residual=actual -predicted value

=110 -89.9085

=20.0915

Solutionc:

size of typical error is 19.27

Solutiond:

Source df Sum Sq Mean Sq F value p-value model 1 12.3 0.001296 residuals 34 total 35

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