A diligent statistics student recorded the length of hisfaithful #2 pencil as he worked away on his homework.He discovered a strong linear relationship between thenumber of hours that he worked and the length of hispencil. Here is the regression analysis for these data.Dependent variable: length (cm)R2 = 92.3, R2 1adj2 = 89.5,coeff se t ratio p valueconstant 17.047 0.128 23.58 60.0001time (hr) -1.914 0.047 35.28 60.0001 a) Write the equation of the least square regressionline.b) Interpret R2 in this context.c) Interpret the equation in this context.d) This student’s girlfriend tried out his model on apencil she had used for 5 hours, and found a residualof -0.88 cm. How long was her pencil at that time?e) Should she have expected this model to describe therate for her pencils? Why or why not?
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.
faithful #2 pencil as he worked away on his homework.
He discovered a strong linear relationship between the
number of hours that he worked and the length of his
pencil. Here is the
Dependent variable: length (cm)
R2 = 92.3, R2
coeff se t ratio p value
constant 17.047 0.128 23.58 60.0001
time (hr) -1.914 0.047 35.28 60.0001
line.
b) Interpret R2
c) Interpret the equation in this context.
d) This student’s girlfriend tried out his model on a
pencil she had used for 5 hours, and found a residual
of -0.88 cm. How long was her pencil at that time?
e) Should she have expected this model to describe the
rate for her pencils? Why or why not?
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