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Hadeel ALI 4/8/2023 BIAM110 DeVry University PRO: Joylene Hall Lab Assignment Information—Introduction to R

Simple linear regression is the least squares calculation of a linear regression model with one explanatory variable. In other words, simple linear regression is a straight line that passes through a set of points in such a way that the sum of the squares of the remaining points of the model (that is, the vertical distances between the remaining point and the line) is as small as possible. This refers to the fact that regression is one of the simplest techniques used in the field of statistics as the slope of the line is equal to the relationship between y and x corrected by the ratio of the standard deviations of these variables. The point where the line intersects the y-axis is the center of mass of the (x, y) data points. Other regression methods exist besides simple least squares (see linear regression). When a person wants to do the regression by eye, he usually tends to draw a slightly sharp line close to that which would result from the least squares method. This happens because it is more natural for the human mind to notice the distances perpendicular to the regression line rather than vertical ones as it happens in the method of least squares. The set of symbols that can be used in R names depends on the operating system and the country that R is running in (technically the language used). Normally all alphanumeric characters are allowed (and in some countries this includes accented characters) plus "." With the restriction that the name must begin with the letter “.” or a letter, and if it begins with a “.” The number must not be the second letter. Names are effectively unlimited in length. Elementary commands consist of expressions or designations. If an expression is given as a command, it will be evaluated and printed (unless specifically invisible),

and the value will be lost. The assignment also evaluates an expression and passes the value to a variable, but the result is not printed automatically. Commands are separated by either a semicolon ("") or a new line. Raw commands can be grouped together into a single compound expression by means of parentheses ("{" and ""). Comments can be placed almost anywhere, starting with a hash sign (""), everything up to the end of a line is a comment. If a command doesn't complete at the end of a line, R will give a different prompt by default which is the plus sign + in the second line and the suffix, continue in reading the entry until the command is grammatically complete. The user can change this prompt. We will generally omit the continuity prompt and denote continuity with a slight indentation. Command lines entered the console are limited to about 4095 bytes and not immediately. In machine learning, computer programs called algorithms analyze large data sets and work backwards from that data to calculate a linear regression equation. Data scientists first train the algorithm on known or named data sets and then use the algorithm to predict the unknown values. Real life data is more complex than the previous example. This is why linear regression analysis must mathematically adjust or transform data values to achieve the following four hypotheses. linear relationship There must be a linear relationship between the independent and dependent variables. To determine this relationship, data scientists create a scatterplot, a random set of x and y values, to see if they lie along a straight line. If not, you can apply nonlinear functions such as square

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root or logarithm to mathematically create a linear relationship between the two variables. remaining independence Data scientists use residual values to measure prediction accuracy. The residual value is the difference between the observed data and the expected value. The remaining values should not have a recognizable pattern between them. For example, you don't want the residual values to get larger over time. You can use various mathematical tests, such as the Durbin-Watson test, to determine residual independence. You can use dummy data to replace any form of data, such as seasonal data. Normal life Graphing methods such as Q-Charts determine whether the residual values are normally distributed. The remaining values should lie along a diagonal line in the center of the graph. If the remaining values are not normalized, you can test the data for random outliers or atypical values. Removing outliers or performing nonlinear transformations can solve the problem. disparity symmetry the symmetry of variance assumes that the remaining values have a constant variance, or standard deviation, from the mean for each value of x. If not, the analysis results may not be accurate. If this assumption is not true, you may have to change the dependent variable. Since variance occurs naturally in large data sets, it makes sense to change the scale of the dependent variable. For example, instead of using population size to predict the number of fire stations in a city, population size might be used to predict the number of fire stations per person.

What are the types of linear regression? Some types of regression analysis are better suited to working with complex data sets than others. Here are some examples. Simple linear regression Simple linear regression is defined by the following linear function: Y = β0 * X + β1 + ε where β0 and β1 are unknown constants representing the regression curve, while ε (epsilon) is the error duration. You can use simple linear regression to model the relationship between two variables, such as: precipitation and crop yield Age and height in children temperature and volume increase of the metallic mercury in a thermometer Multiple linear regression In multiple linear regression analysis, a data set contains a dependent variable and several independent variables. The linear regression line function changes to include more factors as follows: Y= β0*X0 + β1X1 + β2X2+…… βnXn+ ε As the number of prediction variables increases, the β constants also correspondingly increase. Multiple linear regression models that include several variables and their effect on the result as follows: Precipitation, temperature, and fertilizer use on crop yields Diet and exercise on heart disease Increase wages and inflation on housing loan rates Logistic regression Data scientists use logistic regression to measure the probability of an event occurring. An expectation is a value between 0 and 1, where 0 indicates an event that is not likely to occur, and 1 indicates the most likely event. Logistic equations use logarithmic functions to calculate the regression line. Here are some examples: The probability of winning or losing sports match The probability of passing or failing the test The probability that the image is a fruit or an animal.

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