# Report Properties
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MATH253-CWI-Spring14-BMay-Final Project-How Many Red Fruit Snacks are in a Package of Fruit Snacks Part 2

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- 140506-001109 (for reference)

How Many Red Fruit Snacks (cont.)

1. Construct scatter plots

Overlay Polynomial Order 1

Result 1: Scatter Plot-polynomial order 1   [Info]

Overlay Polynomial Order 2

Result 2: Scatter Plot-polynomial order 2   [Info]

Overlay Polynomial Order 3

Result 3: Scatter Plot-polynomial order 3   [Info]

Overlay Polynomial Order 4

Result 4: Scatter Plot polynomial order 4   [Info]

1. Calculate r
 Correlation between (X)Total per pk. and (Y)Total red per pk. is: 0.16113612(0.2636)

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 P-value 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 r2(coefficient of determination)

r2 = 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 y-value

8.      Perform a simple linear regression Highlight the linear equation (model) of best fit, as well as r and r2.

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

R-sq = 0.025964848

Estimate of error standard deviation: 1.4836844

Parameter estimates:

 Parameter Estimate Std. Err. Alternative DF T-Stat P-Value Intercept 1.4366667 0.98042992 ≠ 0 48 1.4653436 0.1493 Slope 0.10833333 0.095771417 ≠ 0 48 1.1311656 0.2636

Analysis of variance table for regression model:

 Source DF SS MS F-stat P-value Model 1 2.8166667 2.8166667 1.2795356 0.2636 Error 48 105.66333 2.2013194 Total 49 108.48

1. The x-value is that I am predicting is 10 and the corresponding y-value is that there are 3 red fruit snacks in each package, since the mean is 2.52. I am choosing the x-value because that is how many are in each package.
2. 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

R2=0.0223

Linear:

y=0.1083x+1.4367

R2=0.026

y=0.0748x2-1.5028x+9.7036

R2=0.056

11.   Use your graphs and highlighted the r2 values to support

The best fit would be the Polynomial/Quadratic model. Yet the r2 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 r2 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.