Last year, five randomly selected students took a math aptitude test before they began their statistics course. The Statistics Department would like to analyze the relationship of the data, make predictions using the regression equation and validate the regression equation. The data of the math aptitude test score and corresponding statistics grade are shown in Table 4. Table 4 Score on math aptitude test (x)Statistics grade (y) 95 85 85 80 80 75 70 75 60 65 Answers at 2 decimal places. ( α) Calculate Σα, Συ, Σay and Σα . Ex = Ey = Exy = Ex2 = (b) Calculate the value of b and bo. bo = (c) Based on your answers in (a) and (b), what linear regression equation best predicts statistics performance, based on math aptitude scores? ŷ =
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.
 alt="Last year, five randomly selected students took a math aptitude test before they began their
statistics course.
The Statistics Department would like to analyze the relationship of the data, make predictions
using the regression equation and validate the regression equation. The data of the math
aptitude test score and corresponding statistics grade are shown in Table 4.
Table 4
Score on math aptitude test (x)Statistics grade (y)
95
85
85
80
80
75
70
75
60
65
Answers at 2 decimal places.
(α) Calculate Συ, ΣΥy Σεy and Σα?.
Ex =
Ey =
Exy =
Ex² =
%3D
(b) Calculate the value of b and bo.
b =
bo =
%3D
(c) Based on your answers in (a) and (b),
what linear regression equation best predicts statistics performance,
based on math aptitude scores?
ŷ =
(d) If a student made an 65 on the aptitude test,
what grade would we expect her to make in statistics?
Grade in Stat =
(e) Find the values of SSR, SST and R2.
SSR =
SST =
R² =
(f) Based on your answer in (e),
how well does the regression equation fit the data?
A coefficient of determination equal to 0.93 indicates that
about 93% of the variation in statistics grades (the dependent variable)
can be explained by the relationship to math aptitude scores (the independent variable).
This would be considered a bad fit to the data / god fit to the data
in the sense that it would substantially improve an educator's ability
to predict student performance in statistics class.
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