How to Analyze the Regression Analysis Output from Excel

The Barbie Bungee lab was conducted in order to find the association between the amount of rubber bands and the distance the Barbie bungeed. Before performing the final experiment, the group conducted an initial investigation to get data that could be analyzed to examine the comparison from the amount of rubber bands to the length Barbie was able to bungee. In the investigation rubber bands would gradually be added one by one starting at two rubber bands. Each time a rubber band was added, three trial bungees were done and the lengths the barbie dropped were recorded. Using data collected from our background investigation, the group used excel to create a sheet displaying the data in a table, a graph showing the correlation constant, the line of best fit. The line of best fit was in slope-intercept form (y=mx+b) where y represents the length of the trial average; m represents the slope

17 In regression analysis, the coefficient of determination R2 measures the amount of variation in y

* Correlation coefficient (R-squared) – This represents how well the independent variables (X) explain the response variable (Y).

Linear regression is an approach for modeling the relationship between a scalar dependent variable Y and explanatory variables (or independent variables) denoted X. Function $f(X,W)=Y$ (shown below) can be learned to predict future values.

Testing allows the p-value that represents the probability showing that results are unlikely to occur by chance. A p-value of 5% or lower is statistically significant. The p value helps in minimizing Type I or Type II errors in the dataset that can often occur when the p value is more than the significance level. The p value can help in stopping the positive and negative correlation between the dataset to reject the null hypothesis and to determine if there is statistical significance in the hypothesis. Understanding the p value is very important in helping researchers to determine the significance of the effect of their experiment and variables for other researchers

Initially, 8 pennies were added to the cup, followed by the addition of 7 pennies and 1 dime, then 4 pennies and 4 dimes, and finally 8 more pennies. There were therefore a total of 27 pennies and 5 dimes added to the cup. Table 2 demonstrates that the force (N) for dimes and pennies went up by almost 0.20 N at each interval. Therefore, the force (N) in Table 2 did not deviate much from the force (N) seen in Table 1 where all pennies were used. The reason little variation in force was seen in Table 2 was due to mostly pennies being added to the cup. Due to so many pennies being added, the dimes had little impact on the overall force (N). If roughly an equal ratio of pennies to dimes had been added to the cup, a more distinct variation between the slope’s in Figure 1 and Figure 2 would have been seen. However, the slope or the average weight of the coins, as represented in Figure 2, was 0.0249 N. The slope can be calculated by dividing the change in the force by the change in the # of pennies and dimes. The x-values represent the number of pennies and dimes, while the y-values represent force (N). The y-intercept value is equal to 0, therefore, the linear equation is y=0.0249x+0. After plotting the line on a manual curve fit, as can be seen in Figure 2, the R2 value was 0.99884. This R2 value is very close to 1, meaning that the match of the linear model to the data fits. After running a

In this study, t= -3.15 describes the mental health variable. It is significant because they are the variables being tested since the p value is 0.002 and the alpha is 0.05, the difference can cause the null hypothesis to be rejected.

Since the P-value (0.386) is greater than the significance level (0.05), we fail to reject the null hypothesis. The p-value implies the probability of rejecting a true null hypothesis.

With a P-value of 0.00, we have a strong level of significance. No additional information is needed to ensure that the data given is accurate.

True or False: Correlations are used to help identify the relationship between two variables. For

Coefficient of determination is the percentage of the variation in the _ variable that results from the _ variable.

So, we should reject the null hypothesis H0. At a 0.05 level of significance level, we conclude that there is a significant difference between the average height for females and the average height for the males.

P-value represents a decimal between 1.0 to below .01. Unfortunately, the level of commonly accepted p-value is 0.05. The level of frequency of P>0.05 means that there is one in twenty chance that the whole study is just accidental. In other words, that there is one in twenty chance that a result may be positive in spite of having no actual relationship. This value is an estimate of the probability that the result has occurred by statistical accident. Thus, a small value of P represents a high level of statistical significance and vice

This regression equation can be graphed as follows assuming β0 as the intercept and β1 as the slope:

But we also have to have measures to see how well the equation explains the relationship be-tween the dependent variables and the independent variables. Studenmund focuses on two techniques. The first is by analysing the R2. This captures “how much of the variation of the dependent variable is explained by the estimated regression equation.” (Studenmund, p.47) The value of R2 can be between 0 and 1 and the higher is the value the closer the estimated equation fits the sample data. In fact a better measure of R2 is R-bar squared as it takes into account the degrees of freedom in the model. However, he notes that R-bar squared alone is not enough to explain the success of our model. There could be other factors so, it is an im-portant estimate but not in we can fully rely on. He also warns