You have been asked to find if there is a correlation between the amount of calories per serving in a bowl of cereal versus the amount of sugar (in grams) in the cereal.  The following data has been given for examination. Sugar Calories 182002321012170121903722019175232012221032210111901119729205a.    Create a scatterplot of the given data.  Be sure you explain your decision on which variable is the predictor and which variable is the response.  b.    Using computer software, calculate the correlation coefficient and interpret what this value implies in relation to the data set. c.    Create a regression equation that models the data and describe the values of the slope and y-intercept with the data set. d.    Predict if a box of cereal has 25 grams of sugar per serving how many calories it will contain. e.    Predict if a box of cereal has 230 calories per serving how much sugar (in grams) it will contain. f.    Discuss any lurking variables could be relevant to analysis of this data set.

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Asked Nov 8, 2019
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You have been asked to find if there is a correlation between the amount of calories per serving in a bowl of cereal versus the amount of sugar (in grams) in the cereal.  The following data has been given for examination.

Sugar

Calories

18

200

23

210

12

170

12

190

37

220

19

175

23

201

22

210

32

210

11

190

11

197

29

205



a.    Create a scatterplot of the given data.  Be sure you explain your decision on which variable is the predictor and which variable is the response. 
b.    Using computer software, calculate the correlation coefficient and interpret what this value implies in relation to the data set.
c.    Create a regression equation that models the data and describe the values of the slope and y-intercept with the data set.
d.    Predict if a box of cereal has 25 grams of sugar per serving how many calories it will contain.
e.    Predict if a box of cereal has 230 calories per serving how much sugar (in grams) it will contain.
f.    Discuss any lurking variables could be relevant to analysis of this data set.


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Expert Answer

Step 1

Note:

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Step 2

a.

Step-by-step procedure to obtain a scatter plot using Excel add-in Mega stat as follows:

  • Enter the data into Excel spreadsheet.
  • Choose Mega Stat > Correlation/Regression > Scatterplot.
  • In Input ranges, enter the values of horizontal axis, Vertical axis, and chart title.
  • Check the appropriate options in Display.
  • Click OK.

The output obtained using Excel add-in Mega stat is represented as follows:

From the above graph, the correlation between the sugar (Predictor) and Calories (Response) are positive.

As grams of sugar increases in the box of cereals then Calories also increase in the same direction.

 

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scatter plot 230 220 210 200 190 180 y 1.258 x+172.073 R2-0.539 170 160 150 10 15 35 25 Sugar 40 30 20 Calories

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Step 3

b.

The correlation coefficient can be obtained as follows:

Step-by-step procedure to obtain the correlation Excel add-in Mega stat as follows:

  • Choose Mega Stat > Correlation/Regression > Regression.
  • In Input ranges, enter the values of Sugar in independent variable.
  • In Input ranges, enter the values of Calories in dependent variable
  • Check the appropriate options in Display.
  • Click OK.

The output obtained using Exc...

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Regression Analysis 0.539 n 12 k 1 r 0.734 Std. Error 10.565 Dep. Var. Calories ANOVA table Source Regression 1,303.4058 Residual 1,116.2608 Total SS MS p-value 0066 F df 1 1,303.4058 11.68 10 11 111.6261 2,419.6667 Regression output vaniables coefficients std. error Intercept Sugar confidence interval t (df=10) p-value 95% lower 95% upper 20.927 1.38E-09 153.7522 3.417 172.0734 8.2227 190.3946 1.2575 0.3680 0066 0.4375 2.0775

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