1. Consider the following data for two variables, x and y.x 22 24 26 30 35 40y 12 21 33 35 40 36a. Develop an estimated regression equation for the data of the form yˆ = b0 + b1x.b. Use the results from part (a) to test for a significant relationship between x and y.Use a = .05.c. Develop a scatter diagram for the data. Does the scatter diagram suggest an estimatedregression equation of the form yˆ = b0 + b1x + b2x2? Explain.d. Develop an estimated regression equation for the data of the form yˆ = b0 + b1x +b2x2.e. Refer to part (d). Is the relationship between x, x2, and y significant? Use a = .05.f. Predict the value of y when x = 25.
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. Consider the following data for two variables, x and y.
x 22 24 26 30 35 40
y 12 21 33 35 40 36
a. Develop an estimated regression equation for the data of the form yˆ = b0 + b1x.
b. Use the results from part (a) to test for a significant relationship between x and y.
Use a = .05.
c. Develop a
regression equation of the form yˆ = b0 + b1x + b2x2
? Explain.
d. Develop an estimated regression equation for the data of the form yˆ = b0 + b1x +
b2x2
.
e. Refer to part (d). Is the relationship between x, x2
, and y significant? Use a = .05.
f. Predict the value of y when x = 25.
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