Simple linear regression questions and answers

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# Simple linear regression questions and answers

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Skip to content. There are several questions I want my students to understand and master in this chapter on Linear Regression : What are the four assumptions of linear regression simple linear and multiple? What is meant by dependent and independent variables? What is difference between regression model, and estimated regression equation?

### Exam Questions – Regression

What is a residual? How is it computed? How do you interpret b1 in multiple linear regressions? What happens when p value for f test is lower than alpha i. What happens when p value for t test is lower than alpha i.

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What is the difference between coefficient of determination, and coefficient of correlation? What does coefficient of determination explain? How to find f test and t test p values? How to write estimated regression equation from coefficient output? What is adjusted R 2? How to compute R 2? When do you reject H0 and when do you fail to reject H0 — for f and t tests? Estimate y for any particular value of x. Consider the x and y units while estimating the y value. Leave a Reply Cancel reply Your email address will not be published.It is a common practice to test data science aspirants on commonly used machine learning algorithms in interviews. These conventional algorithms being linear regression, logistic regression, clustering, decision trees etc.

Data scientists are expected to possess an in-depth knowledge of these algorithms. We consulted hiring managers and data scientists from various organisations to know about the typical ML questions which they ask in an interview. Based on their extensive feedback a set of question and answers were prepared to help aspiring data scientists in their conversations.

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In simple terms, linear regression is a method of finding the best straight line fitting to the given data, i. In technical terms, linear regression is a machine learning algorithm that finds the best linear-fit relationship on any given data, between independent and dependent variables.

## Using Statistical Regression Methods in Education Research

It is mostly done by the Sum of Squared Residuals Method. Feature engineering is the process of transforming raw data into features that better represent the underlying problem to the predictive models, resulting in improved model accuracy on unseen data. In layman terms, feature engineering means the development of new features that may help you understand and model the problem in a better way.

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Feature engineering is of two kinds — business driven and data-driven. Business-driven feature engineering revolves around the inclusion of features from a business point of view. The job here is to transform the business variables into features of the problem.

In case of data-driven feature engineering, the features you add do not have any significant physical interpretation, but they help the model in the prediction of the target variable. To apply feature engineering, one must be fully acquainted with the dataset. This involves knowing what the given data is, what it signifies, what the raw features are, etc. You must also have a crystal clear idea of the problem, such as what factors affect the target variable, what the physical interpretation of the variable is, etc.

What is the use of regularisation? Explain L1 and L2 regularisations. Regularisation is a technique that is used to tackle the problem of overfitting of the model.There are 15 questions here. Click the relevant box or drag and drop the answers as appropriate! A researcher wants to perform a simple linear regression to find out if the socio-economic status of a teacher can predict whether they work at a primary or a secondary school.

Because there are not enough variables for the analysis Because socio-economic status can not be used as a predictor variable Because the outcome variable is nominal not continuous.

Please use the table to decide which of the following statements are true about truancy rates and gender. There are more males than females included in the sample.

Lecture 5 - Linear Regression

Females appear to be disproportionately likely to have been truant in comparison to males. The table shows a statistically significant difference between male and female exclusion rates. Can we conclude that males are more likely to have been truant in the last 12 months than females?

Yes No Not enough information. Please indicate which of the statements about the following graph is true. Can the researcher conclude that test anxiety is significantly associated with test performance? Yes No. If a study found that there was a statistically significant strong positive correlatation between attitude to Maths and exam scores it could be concluded that a positive attitude causes better performance.

True False. When data is nominal When data is continuous When data is ordinal. Please match each of the terms below with their definition. The variable the regression model predicts. The difference between an actual outcome value and the value predicted by the model.

Represents how much of the outcome the regression model explains. Please match the explanations with the figures in the boxes by dragging and dropping each one — note each figure may have more than one matching explanation. The value of Y when X is 0 intercept.Linear regression and modelling problems are presented along with their solutions at the bottom of the page.

Also a linear regression calculator and grapher may be used to check answers and create more opportunities for practice. Free Mathematics Tutorials. About the author Download E-mail. Linear Regression Problems with Solutions Linear regression and modelling problems are presented along with their solutions at the bottom of the page.

Review If the plot of n pairs of data xy for an experiment appear to indicate a "linear relationship" between y and x, then the method of least squares may be used to write a linear relationship between x and y. Figure 1. Formulas for the constants a and b included in the linear regression. Problem 4 The sales of a company in million dollars for each year are shown in the table below. Solutions to the Above Problems a Let us organize the data in a table. Figure 3. Graph of linear regression in problem 1. Figure 4. Graph of linear regression in problem 2. Using t instead of x makes the numbers smaller and therefore manageable. The table of values becomes.

Linear Least Squares Fitting. Privacy Policy. Search website. Problem 3 The values of y and their corresponding values of y are shown in the table below x.A college bookstore must order books two months before each semester starts. They believe that the number of books that will ultimately be sold for any particular course is related to the number of students registered for the course when the books are ordered.

They would like to develop a linear regression equation to help plan how many books to order. From past records, the bookstore obtains the number of students registered, X, and the number of books actually sold for a course, Y, for 12 different semesters. These data are below. Carefully explain what the p-value found in part A means. Fully interpret the strength of the straight-line relationship. Give the regression equation, and interpret the coefficients in terms of this problem.

If appropriate, predict the number of books that would be sold in a semester when 30 students have registered. If appropriate, estimate the average number of books that would be sold in a semester for all courses with 30 students registered. If appropriate, predict the number of books that would be sold in a semester when 5 students have registered. The following scatterplot with the fitted line was obtained using StatCrunch. As the number of students registered for the course increases, the number of books sold by the bookstore appears to increase in a straight-line manner.

H a : The number of students registered and the number of books sold are correlated. Interpretation: At the. Since the p-value is less than 0. This relationship is quite strong. When no students have registered for a course, the number of books sold is 9. It is not particularly meaningful in this problem since all the classes sampled had more than 25 students registered.

For each additional student registered for a course, the number of books sold increases by 0. Since 30 students is within the range of the sampled number of students, it is appropriate to make this prediction. From Minitab the calculated prediction interval is Since 30 students is within the range of the sampled number of students, it is appropriate to make this estimation.

From Minitab the calculated confidence interval is Since 5 students is not within the range of the sampled number of students, it is not appropriate to use the regression equation to make this prediction.

We do not know if the straight-line model would fit data at this point, and we should not extrapolate. Analysis of variance table for regression model:. X value.From a marketing or statistical research to data analysis, linear regression model have an important role in the business. As the simple linear regression equation explains a correlation between 2 variables one independent and one dependent variableit is a basis for many analyses and predictions.

Apart from the business, LR is used in many other areas such as analyzing data sets in statistics, biology or machine learning projects and etc. In our previous post linear regression modelswe explained in details what is simple and multiple linear regression.

Here, we concentrate on the examples of linear regression from the real life. You have to study the relationship between the monthly e-commerce sales and the online advertising costs.

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You have the survey results for 7 online stores for the last year. We can see that there is a positive relationship between the monthly e-commerce sales Y and online advertising costs X. The positive correlation means that the values of the dependent variable y increase when the values of the independent variable x rise. So, if we want to predict the monthly e-commerce sales from the online advertising costs, the higher the value of advertising costs, the higher our prediction of sales.

The Scatter plot shows how much one variable affects another. It shows their correlation. Linear regression aims to find the best-fitting straight line through the points. The best-fitting line is known as the regression line.

If data points are closer when plotted to making a straight line, it means the correlation between the two variables is higher. In our example, the relationship is strong. The slope of This was a simple linear regression example for a positive relationship in business. You have to examine the relationship between the age and price for used cars sold in the last year by a car dealership company.

With an estimated slope of — The above simple linear regression examples and problems aim to help you understand better the whole idea behind simple linear regression equation. Problem-solving using linear regression has so many applications in business, social, biological, and many many other areas. Download the following infographic in PDF with the simple linear regression examples:. Silvia Vylcheva has more than 10 years of experience in the digital marketing world — which gave her a wide business acumen and the ability to identify and understand different customer needs.

Silvia has a passion and knowledge in different business and marketing areas such as inbound methodology, data intelligence, competition research and more.

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I really enjoy your article, seems to me that it can help to many students in order to improve their skills. Save my name, email, and website in this browser for the next time I comment. Currently you have JavaScript disabled. In order to post comments, please make sure JavaScript and Cookies are enabled, and reload the page. Click here for instructions on how to enable JavaScript in your browser. This site uses Akismet to reduce spam. Learn how your comment data is processed. Data Science. Simple Linear Regression Examples. On this page: Simple linear regression examples: problems with solutions. Infographic in PDF In our previous post linear regression modelswe explained in details what is simple and multiple linear regression.

Simple linear regression allows us to study the correlation between only two variables: One variable X is called independent variable or predictor.There is tremendous scope for data scientists and data analysis in the industry today.

The companies recruiting these data scientists would naturally interview them to understand their capability. Let us begin with a fundamental Linear Regression Interview Questions. In simple terms, linear regression is adopting a linear approach to modeling the relationship between a dependent variable scalar response and one or more independent variables explanatory variables. In case you have one explanatory variable, you call it a simple linear regression.

In case you have more than one independent variable, you refer to the process as multiple linear regressions. There are three crucial assumptions one has to make in linear regression. They are. Heteroscedasticity is the exact opposite of homoscedasticity. It entails that there is no equal distribution of the error terms. You use a log function to rectify this phenomenon.

In linear regressionyou use both these values for model validation. However, there is a clear distinction between the two. R square accounts for the variation of all independent variables on the dependent variable. In other words, it considers each independent variable for explaining the variation. In the case of Adjusted R square, it accounts for the significant variables alone for indicating the percentage of variation in the model.

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By significant, we refer to the P values less than 0. We have seen some of the basic interview questions on linear regression. As we move further into the article, we shall look at some of the complex linear regression interview questions as well. You can do so in many ways. Outliers have great significance in linear regression because regression is very sensitive to outliers.

Therefore, it becomes critical to treat outliers with appropriate values. It can also prove useful if you replace the values with mean, median, mode or percentile depending on the distribution. An outlier is an observation point distant from other observations. It might be due to a variance in the measurement. It can also indicate an experimental error. Under such circumstances, you need to exclude the same from the data set. If you do not detect and treat them, they can cause problems in statistical analysis. 