An educational consultant collected data from 10 school districts. Measures were taken of the number of hours per week of instructional time that were allocated to reading instruction at the district level (X) and the district mean achievement in reading (Y). Summary values from the raw data are given as follows: ∑X= 58, ∑Y= 60, ∑X²= 410 ∑Y²= 398, ∑XY= 299 Set up the regression equation for the prediction of Y from X. Determine the standard error of estimate for predicting Y. If X = 9, what will be the predicted value of Y? Determine 95% confidence interval for the predicted value of Y for X = 9.
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.
- An educational consultant collected data from 10 school districts. Measures were taken of the number of hours per week of instructional time that were allocated to reading instruction at the district level (X) and the district mean achievement in reading (Y). Summary values from the raw data are given as follows:
∑X= 58, ∑Y= 60, ∑X²= 410 ∑Y²= 398, ∑XY= 299
- Set up the regression equation for the prediction of Y from X.
- Determine the standard error of estimate for predicting Y.
- If X = 9, what will be the predicted value of Y?
- Determine 95% confidence interval for the predicted value of Y for X = 9.
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