You must respond to at least 2 other students outside your initial thread. Responses should be a minimum of 50 words and may include direct questions.
Peer response #1 – Looking at your peer’s Excel output, and the Regression Equation they wrote out, interpret the slope of their Regression Equation. Use their Regression Equation to make a prediction and show the work for your predicted value based on your expression. For Example, if your peer used Year to predict Price, plug in a Year value into the regression equation and use it to predict the Price of a vehicle. Does this predicted Price value make sense with their data?
Peer response #2 – It is important to remember that typically a two-factor regression model cannot accurately describe the entire situation. Look at the dependent variable that your peer chose. Name at least 2 independent factors you would use to run a Multiple Linear Regression (MLR) and explain why you feel they are related. Then use those factors to run a Multiple Linear Regression (MLR) on your peer’s data and see if the variables you chose are related to the dependent variable they chose. What is your MLR equation? Is your MLR significant? Are any of the Independent factors significant? What is the R2 value? Explain and interpret this value and how it relates to the MLR. Make sure you include your MLR Excel output as an attachment in your response post.
Forum Post 1:
Good Evening Class,
Regression and Correlation seemed to the lesson that made the most sense to me. My attachment has extra information due to the fact of The StatsPlus on my Macbook being different from the normal one. My hypothesis is that there is a positive relationship between the MPG for the city as well as the highway. I believe that a Toyota SUV with a higher city mileage will also show a higher highway mileage. My independent variable is MPG for the city and the dependent variable is MPG for the highway. I believe the numbers will be similar based on each individual vehicle. The correlation or R has a positive correlation of 87.65% and the R2 is 76.82%. This indicates that the SUVs MPG in the city explains 76.82% of the variation of the MPG on the highway. My P value of 0.00193 is less than the alpha of .05 which makes my independent variable a significant factor of my dependent variable.
QUALITATIVE QUANTITATIVE QUALITATIVE QUALITATIVE QUANTITATIVE
VEHICLE TYPE YEAR MAKE MODEL PRICE
SUV 2019 TOYOTA RAV4 FWD XLE 28420
SUV 2018 TOYOTA HIGHLANDER XLE 32621
SUV 2018 TOYOTA RAV4 XLE 21200
SUV 2018 TOYOTA RAV4 FWD SE 23578
SUV 2018 TOYOTA RAV4 FWD LE 18220
SUV 2019 TOYOTA C-HR XLE 18980
SUV 2017 TOYOTA RAV4 FWD XLE 20220
SUV 2018 TOYOTA RAV4 FWD SE 23578
SUV 2017 TOYOTA RAV4 LIMITED 23980
SUV 2019 TOYOTA HIGHLANDER PLATINUM 39440
Forum Post 2:
For this weeks discussion, I am going to start with a hypothesis that there is a relationship between the city and highway gas mileage. My prediction is that the city and highway gas mileage will be positively correlated, as manufacturing steps to increase fuel efficiency likely increase both – though there are exceptions (Corsair, 2015). I arbitrarily chose the city gas mileage as my independent variable (x), and highway gas mileage as my dependent variable (y). However, with correlation it is just as likely that x influences y as y influencing x (or some other variable influencing both which is why we cannot assume causality with correlation).
In analyzing the data, I found the following results: r = .68, r2 = .46, and F(1,8) = 6.90, p = .03. My regression equation (y-hat = mx + b) is Highway MPG = 1.76 MPG (x) 9.28. Interpreting the data, there is a relatively strong relationship (> .5; Laerd Statistics, n.d.) between city and highway gas mileage that indicates as city gas mileage increases, so does highway gas mileage. This is supported by the results of the analysis of variance, which has a p-value below p = .05 and is, therefore, significant. However, only 46% of the variation between city and highway gas mileage is explained by our model. This is very likely due to the fact that I have an outlier in my data (if I remove the outlier, r = .91 and r2 = .82, a much stronger relationship).
Looking at the model regression line for the original data, for every 1 MPG increase in city gas mileage, highway gas mileage is expected to increase by 1.76 MPG on average. The domain for the data is between 17 and 40, the range of the sample city gas mileage. This means we have to limit our predictions to x-values within that range (Dean & Illowsky, 2009). So, using our regression model, a vehicle with a city gas mileage of 20 MPG would be predicted to have an estimated highway gas mileage of 25.92 MPG.
References
Corsair, H. J. (2015, April). Methods to increase fuel efficiency in post-production automobiles: Final report (Report No. NITC-RR-737). National Institute for Transportation & Communities. https://nitc.trec.pdx.edu/research/project/737
Dean, S., & Illowsky, B. (2009). Quantitative information analysis III. Connexions. https://cnx.org/exports/3bf8156d-2d77-4e24-8c25-f4ba4f7f65ed@1.62.pdf/quantitative-information-analysis-iii-1.62.pdf
Laerd Statistics. (n.d.). Pearson product-moment correlation. https://statistics.laerd.com/statistical-guides/pearson-correlation-coefficient-statistical-guide.php
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