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# Regression and ANOVA Analysis: Prepare Meals, Driving Time (Math Problem Sample)

Instructions:

Use regression and ANOVA to analyze the data below. Write a 2 Page paper summarizing the following points

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Regression and ANOVA analysis
The total number of observations is 12 for all the variables. Below is the explanations of the regression analysis and ANOVA test of the observed data.
Regression analysis
Studying
According to the data observed on studying time, regressing time series with studying the following regression equation results; y = 5.612 + 0.0133 x. The equation shows that there is a positive linear relationship between time period and study time. This equation depicts that the individual has 5.6 minutes of studying that increases as time advances. The coefficient of x is 0.0133 and it implies that as time advances by one period, the time of studying will be increased by 0.0133. This equation has a correlation coefficient of 0.1735 that shows that there is a low positive correlation between time and study time and as time period increases, the study time increases too. There is a coefficient of determination of 0.0301 showing that only 3% of the variations of study time with time series that can be explained by the given data (Edwards, 2011).
Prepare meals
On the other hand, regressing time series with time spent on preparing meals, the following regression equation results; y = 9.2309 – 0.2952 x. The equation shows that there is a negative linear relationship between time period and time spent on preparing meals. This equation depicts that the individual has 9.2 minutes of preparing meals that decreases as time advances. The coefficient of x is -0.2952 and it implies that as time series advances by one period, the time of preparing meals will be decreased by 0.2952. This equation has a correlation coefficient of -0.4487 that shows that there is a moderate negative correlation between time and time spent on preparing meals and as time period increases, the meals’ preparation time reduces. There is a coefficient of determination of 0.2013 showing that only 20% of the variations of meals’ preparation time with time series that can be explained by the given data.
Talking on the phone
Regressing time series with time spent talking on the phone yields the following regression equation; y = 5.6918 + 0.017 x. The equation shows that there is a negative linear relationship between time period and talk time. This equation depicts that the individual has 5.7 minutes of talking on the phone that increases as time advances. The coefficient of x is 0.017 that implies that as time series advances by one period, the talk time will be increased by 0.017. This equation also has a correlation coefficient of 0.2663 that shows that there is a low positive correlation between time series and time spent on talking on the phone and as time period increases, the talk time increases (Edwards, 2011). The coefficient of determination is 0.0709 showing that only 7% of the variations of talk time with time series can be explained by the given data (Edwards, 2011).
Driving time
Regressing time series with driving time yields the following regression equation; y = 7.4558 – 0.0234 x. The equation shows that there is a negative linear relationship between time period and driving time. This equation shows that the individual has 7.5 minutes of driving time that decreases as time advances. The coefficient of x is -0.0234 which implies that as time series advances by one period, the driving time will be decreased by 0.0234. The equation has a correlation coefficient of -0.2152 that shows that there is a low negative correlation between time series and driving time and as time period increases, the driving time reduces. The coefficient of determination is 0.0463 showing that about 5% of the variations of talk time with time series can be explained by the given data.
ANOVA test
The data was then divided into two equal halves of six observations each and below are the ANOVA tables to show the results....
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