Statistics

Linear Regression Project

You are to do some statistical analysis of your own. Collect at least 35 data points from two quantitative variables, that you are interested in analyzing the relationship between. Determine something you wish to be able to predict and a variable you think would be helpful in using to make the prediction. Using the data collected you are expected to:

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Determine a hypothesis of your association and explain

Before you actually collect the data, what do you believe will be the relationship between the two variables. When describing the relationship, think about the major parts of the association (form, direction, strength). Also, mention why you chose each variable to be the explanatory and response variables.

Draw and describe the association

Make a scatterplot of your association and write a description of the association. Be sure to mention the form, direction, and strength of the association. Make sure that your description is in context.

Determine the correlation

Calculate the correlation coefficient of your association and be sure to describe what this means in context.

Develop a linear model for the association

There are various ways for you to determine what the model is, you only have to use one.

Describe the slope of the model.

Be sure to describe the slope using an appropriate ratio of units and in context.

Describe the y-intercept of the model, in context

Be sure to describe what the y-intercept means in context. If it doesn’t make any sense in the context of the problem, explain why.

Draw and describe the residual plot

Look for patterns that may exist in the residual plot. Be sure to note if any patterns exist and what they look like.

Determine the level of confidence in the model

There are many things to consider when determining the level of confidence you have in your model. One of them is the appropriate understanding of the R-squared value. Use this along with other reasoning to determine your level of confidence in the model to make accurate predictions.

Use the model to predict values using actual values and determine the residuals

Collect some additional data that does not exist in your original dataset. For example, send your survey to a few more people, or find some additional data that was unused in your original collection, and use the actual results to compare to what would be predicted based on your linear model.

Compare the findings of each group member’s data to each other

How do the results of each association interact with each other? Are they similar? Different? Do the results contradict or support each other?

Conclude the overall results of your statistical analysis

Be sure to mention whether the model is appropriate

Was the association linear? Was it even appropriate to use a linear model? Were there some outliers?

What you believe might be a better explanatory variable

Would there be something better to help predict what you wanted to know in the y variable?

What you might do differently in a future study

What mistakes did you make? What went well? What did you learn?

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