Four training programs are being considered. The time required for each program is: Program A, 6 hours; Program B, 7 hours; Program C, 8 hours; and Program D, 9 hours. Twelve workers were randomly assigned to the four programs and a week later their production output was recorded. The Minitab output is given below. Production 83 89 86 162 168 159 194 175 64 247 195 99 Training Hours 7 6 7 8 8 9 9 9 6 9 8 6 Regression Analysis: Production versus Training Hours The regression equation is: Production = - 167 + 40.5 Training Hours S = 29.8921 R-Sq = ____ R-Sq (adj) = 72.9% Analysis of Variance Source DF SS MS F F-table value Regression __ ____ ___ ____ ______ Residual Error __ 8935 ___ Total __ 36327 a) Complete ANOVA Table and perform the significance of the regression model? b) What is the estimated production amount attributable to a single additional hour? c) What is the intercept? What is its meaning?
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Four training programs are being considered. The time required for each program is: Program A, 6 hours; Program B, 7
hours; Program C, 8 hours; and Program D, 9 hours. Twelve workers were randomly assigned to the four programs and a
week later their production output was recorded. The Minitab output is given below.
Production 83 89 86 162 168 159 194 175 64 247 195 99
Training Hours 7 6 7 8 8 9 9 9 6 9 8 6
The regression equation is:
Production = - 167 + 40.5 Training Hours
S = 29.8921 R-Sq = ____ R-Sq (adj) = 72.9%
Analysis of Variance
Source DF SS MS F F-table value
Regression __ ____ ___ ____ ______
Residual Error __ 8935 ___
Total __ 36327
a) Complete ANOVA Table and perform the significance of the regression model?
b) What is the estimated production amount attributable to a single additional hour?
c) What is the intercept? What is its meaning?
d) Predict the production rate for 6.5 and 12 hours of training.
e) What percent of the variation in production is due to the number of training hours?
f) What is the standard deviation around the regression line?
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