Are The Great Lakes (Lake Michigan) Being Influenced By The Global Greenhouse Effect? Report Sample
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Graphs, Tables, and Calculations
Line graph showing mean annual air temperature for the period between 1975 and 2013
Line graph showing mean annual water temperature for the period between 1975 and 2013
Scatterplot showing the relationship between mean air temperature and mean water temperature
Summary output table from your linear regression analysis of air temperature through time
Summary output table from your linear regression analysis of water temperature
The hypothesis of interest is to test whether there is a relationship between the water temperature and the air temperature. The null hypothesis states that there is no significant relationship between the water temperature and the air temperature. However, the regression analysis rejects the null hypothesis by showing the there is a positive correlation between the air temperature and water temperature.
The air temperature and water temperature are correlated because the scatter plot shows a positive correlation. As the number of the year increases the two variable increases. This was expected because the study aims to prove that there is a relationship between air and water temperatures. The relationship strength is measured by the correlation coefficient or multiple r. The correlation coefficient of air temperature is 0.097768, implying that the relationship is weak. On the other hand, the correlation coefficient on the water temperature is 0.407109, implying that the relationship is relatively stronger.
The line graphs indicate that the temperature trend in Lake Michigan is significantly increasing as the years elapse. According to the trend lines, the air temperature and water temperature increases with the years. According to the slopes of the trend lines, the average temperature increases over time. The slope of the air temperature trend line is 0.0132 while the slope of the air temperature trend line is 0.0596. This implies that the air temperature increases at a higher rate than the air temperature over the years.
The R-squared analysis or mean air temperature was 0.009559 indicates that the model was not acceptable because it is less than 0.3. The R-square implies that the only 0.95 percent of the variables fit the model. On the other hand, the R-squared of mean water temperature was 0.165738 implies that 16.57 percent of the variables fit into the model. The p-value of both mean water and mean air temperature is 0.000 indicating that both variables are statistically significant at 95 percent confidence level hence null hypothesis is rejected. This supports the conclusion in question 3.
The linear regression provides the qualitative analysis of data the helps the researcher to effectively predict the future using the forecasting techniques. For instance, using the regression analysis, one can predict that the air and water temperature are anticipated to change.
The use of the subset of the raw date might have a significant effect on the conclusion regarding the average temperature changes. Although for the period of 32 years all years were included, the omission of some moths of the year could have a significant impact on the results. For instance, in 1975 the moths of January to June were omitted. During these months that temperatures could have a significant effect on the mean temperature. However, according to the p-values of 0.0000, the model is statistically significant indicating that there is a positive relationship between the air temperature and water temperature.
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