La presentazione spiega i primi passi per l'utilizzo del software di elaborazione statistica Spss. Alcune semplici indicazioni da utilizzare indipendentemente dalla versione posseduta del programma.
Regression analysis models the relationship between variables, including dependent and independent variables. Linear regression models take forms like straight lines, polynomials, trigonometric, and interaction terms. Multiple linear regression is useful for understanding variable effects, predicting values, and dealing with multicollinearity using methods like ridge regression, partial least squares, and stepwise regression. Nonlinear and generalized linear models also describe nonlinear relationships. Multivariate regression involves multiple response variables.
La presentazione spiega i primi passi per l'utilizzo del software di elaborazione statistica Spss. Alcune semplici indicazioni da utilizzare indipendentemente dalla versione posseduta del programma.
Regression analysis models the relationship between variables, including dependent and independent variables. Linear regression models take forms like straight lines, polynomials, trigonometric, and interaction terms. Multiple linear regression is useful for understanding variable effects, predicting values, and dealing with multicollinearity using methods like ridge regression, partial least squares, and stepwise regression. Nonlinear and generalized linear models also describe nonlinear relationships. Multivariate regression involves multiple response variables.
This document provides an example of simple linear regression with one independent variable. It explains that linear regression finds the line of best fit by estimating values for the slope (b1) and y-intercept (b0) that minimize the sum of the squared errors between the observed data points and the regression line. It provides the formulas for calculating the least squares estimates of b1 and b0. The document includes a table of temperature and sales data and a corresponding scatter plot as an example of simple linear regression analysis.
This document provides an overview of regression analysis, including:
- Regression analysis measures the average relationship between variables to predict dependent variables from independent variables and show relationships.
- It is widely used in business to predict things like production, prices, and profits. It is also used in sociological and economic studies.
- There are three main methods for studying regression: least squares method, deviations from means method, and deviations from assumed means method. Examples are provided of calculating regression equations for bivariate data using each method.
The document presents the results of a simple linear regression analysis conducted by a black belt to predict the number of calls answered (dependent variable) based on staffing levels (independent variable) using data collected over 240 samples in a call center. The regression equation found 83.4% of the variation in calls answered was explained by staffing levels. Notable outliers and leverage points were identified that could impact the strength of the predicted relationship between calls answered and staffing.
- Regression analysis is a statistical tool used to examine relationships between variables and can help predict future outcomes. It allows one to assess how the value of a dependent variable changes as the value of an independent variable is varied.
- Simple linear regression involves one independent variable, while multiple regression can include any number of independent variables. Regression analysis outputs include coefficients, residuals, and measures of fit like the R-squared value.
- An example uses home size and price data from 10 houses to generate a linear regression equation predicting that price increases by around $110 for each additional square foot. This model explains 58% of the variation in home prices.
The document provides an overview of regression analysis. It defines regression analysis as a technique used to estimate the relationship between a dependent variable and one or more independent variables. The key purposes of regression are to estimate relationships between variables, determine the effect of each independent variable on the dependent variable, and predict the dependent variable given values of the independent variables. The document also outlines the assumptions of the linear regression model, introduces simple and multiple regression, and describes methods for model building including variable selection procedures.
This document provides an example of simple linear regression with one independent variable. It explains that linear regression finds the line of best fit by estimating values for the slope (b1) and y-intercept (b0) that minimize the sum of the squared errors between the observed data points and the regression line. It provides the formulas for calculating the least squares estimates of b1 and b0. The document includes a table of temperature and sales data and a corresponding scatter plot as an example of simple linear regression analysis.
This document provides an overview of regression analysis, including:
- Regression analysis measures the average relationship between variables to predict dependent variables from independent variables and show relationships.
- It is widely used in business to predict things like production, prices, and profits. It is also used in sociological and economic studies.
- There are three main methods for studying regression: least squares method, deviations from means method, and deviations from assumed means method. Examples are provided of calculating regression equations for bivariate data using each method.
The document presents the results of a simple linear regression analysis conducted by a black belt to predict the number of calls answered (dependent variable) based on staffing levels (independent variable) using data collected over 240 samples in a call center. The regression equation found 83.4% of the variation in calls answered was explained by staffing levels. Notable outliers and leverage points were identified that could impact the strength of the predicted relationship between calls answered and staffing.
- Regression analysis is a statistical tool used to examine relationships between variables and can help predict future outcomes. It allows one to assess how the value of a dependent variable changes as the value of an independent variable is varied.
- Simple linear regression involves one independent variable, while multiple regression can include any number of independent variables. Regression analysis outputs include coefficients, residuals, and measures of fit like the R-squared value.
- An example uses home size and price data from 10 houses to generate a linear regression equation predicting that price increases by around $110 for each additional square foot. This model explains 58% of the variation in home prices.
The document provides an overview of regression analysis. It defines regression analysis as a technique used to estimate the relationship between a dependent variable and one or more independent variables. The key purposes of regression are to estimate relationships between variables, determine the effect of each independent variable on the dependent variable, and predict the dependent variable given values of the independent variables. The document also outlines the assumptions of the linear regression model, introduces simple and multiple regression, and describes methods for model building including variable selection procedures.
2. Progetto 2
• Si considerino i dati salvati nel file pcb.mat
0 2 4 6 8 10 12
6
6.5
7
7.5
8
8.5
9
9.5
10
10.5
11
age
ConcentrazionePCB
Dati sulla
concentrazione di
residui di bifenili poli-
clorinati (PCB) misurati
nelle trote del lago
Cayuga (NY) rispetto
all’età del pesce
Bache CA, Serum JW, Youngs WD and Lisk JD, (1972) “Polychlorinated biphenyl
Residues: Accumulation in Cayuga lake trout with age”, Science, 117, 1192
3. Regressione lineare - Progetto
• Si investighi quale modello lineare nei parametri
è più adeguato per descrivere la relazione tra età
del pescato e concentrazione di PCB nelle sue
carni
• A tal proposito, si possono usare le misure di
adeguatezza che si reputano più adeguate.