Question

Data was obtained from a chemical process where the percent yield of the process is thought to be related to the reaction temperature (in degrees F). We would like to see if the temperature can predict the yield. The regression equation we obtained was Y = 17+ 2X. Use this information for all the parts.

Part 1: What would X be here?

Group of answer choices

Yield, since it is the one being predicted.

Temperature, since it is being used to predict the yield.

The response variable.

Temperature, since is the one being predicted.

Question 40: Part 2: What would the response variable be here?

Group of answer choices

Temperature, since it is the one used to predict yield.

Yield, since it is used to predict temperature.

Yield, since it is the one being predicted.

Temperature, since it is the one being predicted.

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Question 41: Part 3: Interpret the slope of the regression line above.

Group of answer choices

For each additional percent increase in yield, the mean temperature increases by 17 degrees.

For each additional percent increase in yield, the mean temperature increases by 2 degrees.

When the temperature is zero degrees, the yield is 17.

For each degree increase in temperature, the mean yield increases by 2%.

Question 42: Part 4: Interpret the intercept of the regression line above.

Group of answer choices

When the yield increases by 1%, the average temperature increases by 2 degrees.

When the temperature is zero degrees, the average yield is 17%.

When the yield is zero, the average temperature is 17 degrees.

When the temperature increases by one degree, the average yield increases by 2%.

Question 43

Part 5: Use the regression line to predict the yield of the reaction when the temperature is 32 degrees.

Answer 1

Solution

Back-up Theory

In the linear regression model: Y = β₀ + β₁X, Y is the response variable, i.e., the variable being predicted and X is the predictor variable....................................................................……………......................................................................…..…..(1)

Estimated Regression of Y on X is given by: Y_hat = β_0hat + β_1hatX,........................................................................…..……….(2)

where β_0hat and β_1hat are the least estimates of the intercept and slope respectively. ...........................................................(3)

Predicted value for a given value of the predictor variable is obtained by substituting the given value of the predictor variable in (2)............................................................................................................................................................................(4)

β_0hat represents the y-intercept mathematically and physically represents the expected value of the response (dependent) variable when the predictor (independent/explanatory) variable  is zero ...................................................................…………(5)

β_1hat represents the slope of the regression line mathematically and physically represents the expected change (increase/decrease) in value of the response (dependent) variable when the predictor (independent/explanatory) variable changes (increases/decreases) by one unit….….. ................................................................................................................. (6)

Now to work out the solution,

Q40 (?) Part (1)

Vide (1), Temperature, since it is being used to predict the yield. Answer 1

Q40 Part (2)

Vide (1), Yield, since it is the one being predicted. Answer 2

Q41 Part (3)

Vide (6), For each degree increase in temperature, the mean yield increases by 2%. Answer 3

Q42 Part (4)

Vide (5), When the temperature is zero degrees, the average yield is 17%. Answer 4

Q43 Part (5)

Vide (2) and (4), predicted value of the yield of the reaction when the temperature is 32 degrees.is 81% Answer 5 [substitute x = 32 in the given regression line: y = 32 + 2x]

DONE