Acetic acid vs Taste: (e) You should detect one or more potential problems with

Question

Acetic acid vs Taste:

(e) You should detect one or more potential problems with the model
through the work.
(f) Using the new model that was estimated for part (e), find the
95% confidence interval for mean taste when acetic acid has a
value of 4.5.
(g) Are there any other problems remaining with the model after
what was done in part (e)? Justify your answer. Note that you
do not need to actually implement any changes to the model.

taste Acetic 12.3 4.543 20.9 5.159 39 5.366 47.9 5.759 5.6 4.663 25.9 5.697 37.3 5.892 21.9 6.078 18.1 4.898 21 5.242 34.9 5.74 57.2 6.446 0.7 4.477 25.9 5.236 54.9 6.151 40.9 6.365 15.9 4.787 6.4 5.412 18 5.247 38.9 5.438 14 4.564 15.2 5.298 32 5.455 56.7 5.855 16.8 5.366 11.6 6.043 26.5 6.458 0.7 5.328 13.4 5.802 5.5 6.176

Explanation / Answer

(e) You should detect one or more potential problems with the model through the work.

For the given two variables, it was observed that there is a considerable positive linear relationship exists between the two variables taste and acetic. We can find the regression equation for the dependent variable taste based on the independent variable acetic. We have to use regression model for given data. The regression output is given as below:

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.549539299

R Square

0.301993441

Adjusted R Square

0.277064635

Standard Error

13.82123774

Observations

30

ANOVA

df

SS

MS

F

Significance F

Regression

1

2314.141512

2314.14151

12.11423623

0.001658192

Residual

28

5348.745155

191.026613

Total

29

7662.886667

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

-61.49861238

24.84637942

-2.4751539

0.019637301

-112.3941128

-10.60311199

Acetic

15.64776721

4.49577282

3.48055114

0.001658192

6.438594178

24.85694024

(f) Using the new model that was estimated for part (e), find the 95% confidence interval for mean taste when acetic acid has a value of 4.5.

Regression equation is given as below:

Taste = -61.4986 + 15.6478*Acetic

If acetic acid = 4.5

Taste = -61.4986 + 15.6478*4.5

Taste = 8.9165

Critical t = 3.48055114

SE = 4.49577282

Lower limit = 8.9165 - 3.48055114*4.49577282 = -6.731267214

Upper limit = 8.9165 + 3.48055114*4.49577282 = 24.56426721

Confidence interval = (-6.73, 24.56)

(g) Are there any other problems remaining with the model after what was done in part (e)? Justify your answer. Note that you do not need to actually implement any changes to the model.

No, there are no any problems remaining with the model. For the given overall model, it is observed that model is statistically significant as p-value is given as 0.00166. Also, both coefficients are statistically significant.

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.549539299

R Square

0.301993441

Adjusted R Square

0.277064635

Standard Error

13.82123774

Observations

30

ANOVA

df

SS

MS

F

Significance F

Regression

1

2314.141512

2314.14151

12.11423623

0.001658192

Residual

28

5348.745155

191.026613

Total

29

7662.886667

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

-61.49861238

24.84637942

-2.4751539

0.019637301

-112.3941128

-10.60311199

Acetic

15.64776721

4.49577282

3.48055114

0.001658192

6.438594178

24.85694024

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