For waves on a string, there are two formulae for the wave velocity:

For each of the two variables T and f, answer the following:

- How can you increase the value of this variable in the lab?

- Explain what happens (and why) to ,and f as a result of this change.

(The length of the string is a constant).

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Priyanshu PatelLv10

22 Mar 2021

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Opeele Kyinkafa sells different used 2005 GM cars in excellent condition. The value or the retail price (Price) of a car is dependent on a variety of characteristics such as number of miles the car has been driven (Mileage), manufacturer of the car (Make) such as Buick, Cadillac, Chevrolet, Pontiac, SAAB, and Saturn. The car price is also influenced by the body type (Type) such as sedan, convertible, coupe, hatchback and wagon. It is also affected by number of cylinders (Cylinders) in the engine, the engine size (Liter), cruise control which is an indicator variable representing whether the car has cruise control (yes) or no otherwise and Sound indicator representing whether the car has upgraded speakers (yes) or no otherwise. All cars in this data set were less than one year old when priced and considered to be in excellent condition. Determine which major variables are dummies and are dynamic? Identify 3 potential unobserved heterogenous factors in this dataset. Display the full descriptive statistics of the data in R. Why do you think some variables are starred (*)? What is the median for “price”, standard deviation for “mileage”, skewness for “cylinder” and mean for “sound”? Test if “price” is normally distributed using histogram, kernel density plot and the shapiro wilk test. Create a red scatterplot matrix of price, mileage, cylinder, liter, make. From your graph, is the correlation between price & mileage positive or negative? What’s the pearson correlation coefficient between price & mileage and between “cylinder” & “liter” correct to 2 d.p Create a correlation matrix of the dataset by finding the apt R command for converting all string/dummy variables From the matrix, identify 2 potentially good predictors? Identify 3 pairs of variables that are mostly multicollinear. Which 2 pairs of variables are least correlated? Identify 3 pairs of variables most highly correlated with Cylinder Generate a simple regression plot of price on mileage with a re fitted line. Run the whole multiple regression model (label the equation as "regprice") & use it to answer the other questions. Specify the regression model for the whole data keeping the exact names of the variables. Write the estimated regression equation. In one sentence, which variables are significant and which are not? Justify Is the regression model justifiable? Explain Interpret the coefficient of Mileage, MakeCadillac, TypeSedan, Cylinder, & Cruiseyes. Compare the price of a car with 130,000 mileage, 6 cylinders, 3.8 liters, with cruise and sound, was manufactured by Pontiac with a convertible body type with that of the price of a car with four cylinders, 120,000 mileage, 3.8 liters, without cruise nor sound, was manufactured by Cadillac with a hatchback body type. Which factor(s) appears to be causing a comparative difference (if any)? Using only the VIF, which one of the pairs of variables selected to be multicollinear may be deleted? Justify?

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Inalize three research questions relating to your selected dataset. Make sure the variables used in the final questions you select are of the following format:
1. Continuous response and continuous explanatory variable
2. Categorical response and categorical explanatory variable
3. Continuous response and categorical explanatory variable (note: the categorical variable must be dichotomous for this question)
Each research question should have a clear explanatory and response variable. Review, as necessary, the ‘Laerd Statistics’ reading from last week which explains data types and the difference between response variables (also referred to as dependent or outcome variables) and explanatory variables (also referred to as independent or predictor variables).
Then, in your initial post, list your three finalized research questions, indicating the variable types.
For example, using data from the Framingham Heart Study dataset, one question might be: ‘Is there a significant difference in total serum cholesterol levels [TOTCHOL] (continuous-ratio) (response) between smokers and non-smokers [CURSMOKE] (categorical-dichotomous) (explanatory)?’
In your response post to your peers, provide feedback on their finalized research questions, which will become the foundation of each student’s final project. Consider the following questions as you review your peers' research questions:
• Is each research question clearly stated?
• Does each research question relate to the dataset?
• Do the three research questions meet the data type requirements?
• Does each research question identify response and explanatory variables correctly?