1. Regression methods were used to analyze the data from a study investigating the relationship between roadway surface temperature (x) and pavement deflection ( y). Summary quantities were n = 20, ∑ y i = 12.75, ∑ y i 2 = 8.86, ∑ x i = 1478, ∑ x i 2 = 143 , 215.80, and ∑ x i y i = 1083.67. (a) Calculate the least squares estimates of the slope and intercept. Graph the regression line. with plotting of graph (b) Use the equation of the fitted line to predict what pavement deflection would be observed when the surface temperature is 85F. (c) What is the mean pavement deflection when the surface temperature is 90F?
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.
1. Regression methods were used to analyze the data from a study investigating the relationship between roadway surface temperature (x) and pavement deflection ( y). Summary quantities were n = 20, ∑ y i = 12.75, ∑ y i 2 = 8.86, ∑ x i = 1478, ∑ x i 2 = 143 , 215.80, and ∑ x i y i = 1083.67.
(a) Calculate the least squares estimates of the slope and intercept. Graph the regression line. with plotting of graph
(b) Use the equation of the fitted line to predict what pavement deflection would be observed when the surface temperature is 85F.
(c) What is the mean pavement deflection when the surface temperature is 90F?
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