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## Regression and Correlation Responses

INSTRUCTIONS: Provide (2) peer responses for RESPONSES 1 AND 2 below. Attached are RESPONSE 1 and 2 excel work to help you with the responses.

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.

RESPONSE 1:

For this weeks forum on regression and correlation I reviewed the original car data from week 1 and picked the year of the car and the price to show a correlation. I believe the correlation will be positive because the newer the car the price will be more. Since the independent variable (x) predicts the value of (y) in this scenario the intendent value will be the price in correlation to the dependent value of how old the car is (years).

I will be predicting that the price of the car will be more when the age of the car (years) is less.

I added a new column to the original excel data sheet where I adjusted the years and converted them to number of years. Then I correlated the years to the price which comes out to 0.464224032

Since I have a correlation we can find R2 = 0.464224032*0.464224032=0.215503952 = 21.55%

After running a regression analysis on my car data the R2  I found that the R Square did not match my calculations. The regression statistics calculated R2 10.07%

The significant F was 0.405285         a=0.05

To calculate the p-value < a  = 0.405285 < 0.05

Then I calculated the Regression Equation =

Price=slope(years)+price of the car

Coefficients intercept 29897.22 and 2725

2725(0)+29897.22=  29897.22

We can interpret the data by coming to conclusion that each new car will be \$29,897.22

(I had a positive correlation instead of a negative and I would like some input if the statistics is correct).

-Christina

RESPONSE 2:

To start, I chose to see if there was a direct correlation between city MPG and highway (hwy) MPG. I chose this because it was different than any of the PDFs and was challenged by it. Although, towards the end of the exercise, I began to think of all the variables that change from vehicle to vehicle and realized the outcome was going to be harder to explain then I thought.

My =Correl was 0.967713303

Therefore, my R^2 was 0.936469036 = 93.65% or 94% for the sake of the argument. With an R^2 of 94% (vs a 100%) there is a pretty high probability that city MPG is correlated with highway MPG to some extent.

As for my P value, it was 1.944. 1.944 > 0.05 which tells me that there is no good way to compare city MPG to highway MPG between multiple vehicles.

In summary, as we know a vehicle does better on the highway then in the city. However, unless the same vehicles were used in the comparison, there is no good way to compare city MPG with highway MPG from different car makes and models.

Attached you will find my Excel spread sheet with my work.