BIO 500 W6 linear regression line

If a regression line (linear regression line) is said to “fit” the data presented in a scatter plot, what relation is minimized between the observed data, y, and the predicted output for the regression line?

In statistics, linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables). The case of one explanatory variable is called simple linear regression; for more than one, the process is called multiple linear regression.^[1] This term is distinct from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable.^[2]

In linear regression, the relationships are modeled using linear predictor functions whose unknown model parameters are estimated from the data. Such models are called linear models.^[3] Most commonly, the conditional mean of the response given the values of the explanatory variables (or predictors) is assumed to be an affine function of those values; less commonly, the conditional median or some other quantile is used. Like all forms of regression analysis, linear regression focuses on the conditional probability distribution of the response given the values of the predictors, rather than on the joint probability distribution of all of these variables, which is the domain of multivariate analysis.

Linear regression was the first type of regression analysis to be studied rigorously, and to be used extensively in practical applications.^[4] This is because models which depend linearly on their unknown parameters are easier to fit than models which are non-linearly

related to their parameters and because the statistical properties of the resulting estimators are easier to determine.

Linear regression has many practical uses. Most applications fall into one of the following two broad categories:

If the goal is prediction, forecasting, or error reduction,^{[clarification needed]} linear regression can be used to fit a predictive model to an observed data set of values of the response and explanatory variables. After developing such a model, if additional values of the explanatory variables are collected without an accompanying response value, the fitted model can be used to make a prediction of the response.
If the goal is to explain variation in the response variable that can be attributed to variation in the explanatory variables, linear regression analysis can be applied to quantify the strength of the relationship between the response and the explanatory variables, and in particular to determine whether some explanatory variables may have no linear relationship with the response at all, or to identify which subsets of explanatory variables may contain redundant information about the response.

Linear regression models are often fitted using the least squares approach, but they may also be fitted in other ways, such as by minimizing the “lack of fit” in some other norm (as with least absolute deviations regression), or by minimizing a penalized version of the least squares cost function as in ridge regression (L²-norm penalty) and lasso (L¹-norm penalty). Conversely, the least squares approach can be used to fit models that are not linear models. Thus, although the terms “least squares” and “linear model” are closely linked, they are not synonymous.

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Important information for writing discussion questions and participation

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Hello class and welcome to the class and I will be your instructor for this course. This is a -week course and requires a lot of time commitment, organization, and a high level of dedication. Please use the class syllabus to guide you through all the assignments required for the course. I have also attached the classroom policies to this announcement to know your expectations for this course. Please review this document carefully and ask me any questions if you do. You could email me at any time or send me a message via the “message” icon in halo if you need to contact me. I check my email regularly, so you should get a response within 24 hours. If you have not heard from me within 24 hours and need to contact me urgently, please send a follow up text to

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Your initial discussion post should be a minimum of 200 words and response posts should be a minimum of 150 words. Be advised that I grade based on quality and not necessarily the number of words you post. A minimum of TWO references should be used for your initial post. For your response post, you do not need references as personal experiences would count as response posts. If you however cite anything from the literature for your response post, it is required that you cite your reference. You should include a minimum of THREE references for papers in this course. Please note that references should be no more than 5 years old except recommended as a resource for the class. Furthermore, for each discussion board question, you need ONE initial substantive response and TWO substantive responses to either your classmates or your instructor for a total of THREE responses. There are TWO discussion questions each week, hence, you need a total minimum of SIX discussion posts for each week. I usually post a discussion question each week. You could also respond to these as it would count towards your required SIX discussion posts for the week.

I understand this is a lot of information to cover in 5 weeks, however, the Bible says in Philippians 4:13 that we can do all things through Christ that strengthens us. Even in times like this, we are encouraged by God’s word that we have that ability in us to succeed with His strength. I pray that each and every one of you receives strength for this course and life generally as we navigate through this pandemic that is shaking our world today. Relax and enjoy the course!

Hi Class,

Please read through the following information on writing a Discussion question response and participation posts.

Contact me if you have any questions.

Important information on Writing a Discussion Question

Your response needs to be a minimum of 150 words (not including your list of references)
There needs to be at least TWO references with ONE being a peer reviewed professional journal article.
Include in-text citations in your response
Do not include quotes—instead summarize and paraphrase the information
Follow APA-7th edition
Points will be deducted if the above is not followed

Participation –replies to your classmates or instructor

A minimum of 6 responses per week, on at least 3 days of the week.
Each response needs at least ONE reference with citations—best if it is a peer reviewed journal article
Each response needs to be at least 75 words in length (does not include your list of references)
Responses need to be substantive by bringing information to the discussion or further enhance the discussion. Responses of “I agree” or “great post” does not count for the word count.
Follow APA 7th edition
Points will be deducted if the above is not followed
Remember to use and follow APA-7th edition for all weekly assignments, discussion questions, and participation points.
Here are some helpful links
Student paper example
Citing Sources
The Writing Center is a great resource