I have all this information but don\'t really know how to analyze it? Correlatio

Question

I have all this information but don't really know how to analyze it?

Correlation Project

Answer each question with complete sentences and include all relevant JMP files requested.

What are the two variables of interest? What linear relationship are you interested in exploring? Time of day glucose is taken and Glucose levels. I will be exploring Time of day glucose vs Glucose level linear relationship.

Which data collection technique will be used and why is it best?

What sample size is best for this data set and why?

Collect the data. Explain any issues you had during data collection. Include the JMP data file with your submission.

Is there a statistically significant relationship between the two variables? Describe the relationship in terms of strength and direction. Show your work by including the JMP output file.

Develop a linear model of this relationship. Include the JMP output file.

Is this a valid model to describe this relationship? Describe the fit of the model. Include the JMP output file.

Time of day glucose is taken Glucoselevel SUMMARY OUTPUT for combined glucose levels 1 85 1=breakfast Regression Statistics 1 87 2=lunch Multiple R 0.044206067 1 150 3=dinner R Square 0.001954176 1 100 One-way ANOVA: Glucoselevel versus Time of day glucose is taken Adjusted R Square -0.037967657 1 100 Method Standard Error 0.847698645 1 90 Null hypothesis         All means are equal Observations 27 1 70 Alternative hypothesis At least one mean is different 1 72 Significance level      = 0.05 ANOVA 1 75 Equal variances were assumed for the analysis. df SS MS F Significance F 2 70 Regression 1 0.035175175 0.035175175 0.048950066 0.826697554 2 85 Factor Information Residual 25 17.96482483 0.718592993 2 143 Factor                                               Levels Values Total 26 18 2 100 Time of day glucose is taken       3 1, 2, 3 2 121 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% 2 92 Analysis of Variance Intercept 2.132992559 0.622850201 3.424567503 0.002132153 0.850208557 3.415776561 0.850208557 2 66 Source                                             DF   Adj SS    Adj MS    F-Value P-Value Glucoselevel -0.001465632 0.006624428 -0.221246619 0.826697554 -0.015108897 0.012177632 -0.015108897 2 70 Time of day glucose is taken   2     32.1          16.04      0.02         0.977 2 69 Error                                                  24    16343.1     680.96 3 75 Total                                                  26    16375.2 3 80 3 140 Model Summary 3 92       S                  R-sq       R-sq(adj)   R-sq(pred) 3 130 26.0953          0.20%      0.00%           0.00% 3 83 3 70 Means 3 68 When glucose is taken            N Mean SEmean StDev         95% CI 3 67 1 9 92.11           8.12 24.35        (74.16, 110.06) 2 9 90.67          8.91 26.72          (72.71, 108.62) 3 9 89.44          9.04 27.13         (71.49, 107.40)

Explanation / Answer

Here glucose level is independent variable and time of the day glucose taken is dependent variable.

Which data collection technique will be used and why is it best?

Here we use regression technique

Here regression model is,

time of day glucose is taken = 2.13 - 0.001 * glucose level

Here intercept = 2.13

Slope = -0.001

Interpretation of slope : FOr one unit change in glucose level will be 0.001 decrease in time of day glucose is taken.

Here regression coefficient is negative so there is negative relationship between these two variables.

R-sq = 0.00195

It expresses the proportion of variation in time of day glucose is taken which is explained by variation in glucose level.

Here we have to test the hypothesis that,

H0 : B = 0 Vs H1 : B not= 0

where B is population slope for glucose level.

Assume alpha = level of significance = 0.05

Here test statistic follows t-distribution.

In the output,

t = -0.221

And p-value = 0.8267

P-value > alpha

Accept H0 at 5% level of significance.

Conclusion : The population slope for glucose level is differ than 0.

Validity of the model :

We have given multiple r= sample correlation coefficient = 0.044

Now we have to find critical value for taking decision using critical value table of population correlation.

For alpha = 0.05

deg_freedom = n-2 = 27-2 = 25

Critical value = 0.381

Here | r | < Critical value model doesn’t fits good.

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