I contacted the help desk and since my report would keep deleting the Correlation and my Conclusion she suggested that I create 2 reports to fit it all in.
Diana: incident number 140506001109 (for reference)
How Many Red Fruit Snacks (cont.)
 Construct scatter plots
Overlay Polynomial Order 1
Overlay Polynomial Order 2
Overlay Polynomial Order 3
Overlay Polynomial Order 4
 Calculate r
Correlation between (X)Total per pk. and (Y)Total red per pk. is: 
State that value and how you interpret it: The value is greater than a significance level of 0.05, so there is not sufficient evidence to support the claim that there is a linear correlation between how many red fruit snacks there are compared to how many total fruit snacks there are per each package.
How does your Pvalue compare to alpha at a 95% confidence level? Is there enough evidence to support a claim of linear correlation between your x and y variables?
5. My P value is 0.2636 which is higher than the significance level, alpha .05. I will fail to reject Ho and conclude that there is insufficient evidence to support the claim of a linear correlation.
6. Calculate r^{2}(coefficient of determination)
r^{2} = 0.026. I conclude that 0.026 (or about 3%) of the number or red fruit snacks per package can be explained by the linear relationship between the amounts of total fruit snacks per package. This implies that about 97% of the red fruit snacks per package can’t be explained by the total amount of fruit snacks in a package.
7. Part II: Develop a Regression Model of Best Fit and Predict yvalue
8. Perform a simple linear regression Highlight the linear equation (model) of best fit, as well as r and r^{2}.
Simple linear regression results: 


Dependent Variable: (Y)Total red per pk. 


Independent Variable: (X)Total per pk. 


(Y)Total red per pk. = 1.4366667 + 0.10833333x (X)Total per pk. 

Sample size: 50 


R (correlation coefficient) = 0.16113612 


Rsq = 0.025964848 


Estimate of error standard deviation: 1.4836844 


Parameter estimates:



 The xvalue is that I am predicting is 10 and the corresponding yvalue is that there are 3 red fruit snacks in each package, since the mean is 2.52. I am choosing the xvalue because that is how many are in each package.
 Predicted values:
Linear
X value 
Pred. Y 
s.e.(Pred. y) 
95% C.I. for mean 
95% P.I. for new 
10 
2.52 
0.20982466 
(2.0981192, 2.9418808) 
(0.49283124, 5.5328312) 
Polynomial
X value 
Pred. Y 
s.e.(Pred. y) 
95% C.I. for mean 
95% P.I. for new 
10 
2.1607321 
0.36034972 
(1.435802, 2.8856623) 
(0.89595818, 5.2174225) 
Part III: Investigate Nonlinear Regression Models of Correlation and Construct Prediction Intervals
10. Perform at least four nonlinear regressions
I could not get the exponential or power to work with my graphs. These were the only 3 options that would come up in excel.
Logarithmic:
y=1.0549ln(x)+0.1147
R^{2}=0.0223
Linear:
y=0.1083x+1.4367
R^{2}=0.026
Polynomial/Quadratic:
y=0.0748x^{2}1.5028x+9.7036
R^{2}=0.056
11. Use your graphs and highlighted the r^{2 }values to support
The best fit would be the Polynomial/Quadratic model. Yet the r^{2} is very low at .056 so really
there is no good model for a relationship between your data variables.
12. The prediction intervals for each of my models don’t compare by too much since they are all less than .10. The most useful is the polynomial/quadratic since the r^{2 }value is .056. Yes, it is derived from the model that I found to be the best fit.
When all of the tests were performed and documented, I found that the amount of fruit snacks, in particular red fruit snacks, did not have a set amount of colors in each package. There was a package that had three red fruit snacks out of fifteen total, while another package that had five red fruit snacks out of eight total with a lot of different combinations in between. In counting the total amount of fruit snacks it is also apparent that the Target brand and Welches brand have the most fruit snacks in them and also have cheaper prices than the other brands. I would have never known that information had I not had this assignment to do all semester and with four kids that is a great thing to know.
There were some interesting concepts I learned throughout this class such as: what a normal distribution looks like, as well as how to not be fooled by pretty graphs and charts, usually pie charts. It is also important that you take into account how big the sample size is or if there are any outliers because these factors can greatly influence the results and may make them skewed. Also unless you purchase a box of only red fruit snacks, you never know how many red fruit snacks you are going to get.
Already a member? Sign in.