The table below gives the number of hours spent unsupervised each day as well as the overall grade averages for seven randomly selected middle school students. Using this data, consider the equation of the regression line, yˆ=b0+b1xy^=b0+b1x, for predicting the overall grade average for a middle school student based on the number of hours spent unsupervised each day. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Hours Unsupervised 0.50.5 11 2.52.5 33 3.53.5 44 5.55.5 Overall Grades 9999 8787 8686 7979 7272 7171 6565 Step 1 of 6: Find the estimated slope. Round your answer to three decimal places. Step 2 of 6: Find the estimated y-intercept. Round your answer to three decimal places. Step 3 of 6: According to the estimated linear model, if the value of the independent variable is increased by one unit, then the change in the dependent variable yˆy^ is given by? Step 4 of 6: Determine the value of the dependent variable yˆy^ at x=0x=0. Step 5 of 6: Determine if the statement "All points predicted by the linear model fall on the same line" is true or false. Step 6 of 6: Find the value of the coefficient of determination. Round your answer to three decimal places.
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.
The table below gives the number of hours spent unsupervised each day as well as the overall grade averages for seven randomly selected middle school students. Using this data, consider the equation of the regression line, yˆ=b0+b1xy^=b0+b1x, for predicting the overall grade average for a middle school student based on the number of hours spent unsupervised each day. Keep in mind, the
| Hours Unsupervised | 0.50.5 | 11 | 2.52.5 | 33 | 3.53.5 | 44 | 5.55.5 |
|---|---|---|---|---|---|---|---|
| Overall Grades | 9999 | 8787 | 8686 | 7979 | 7272 | 7171 | 6565 |
Find the estimated slope. Round your answer to three decimal places.
Find the estimated y-intercept. Round your answer to three decimal places.
According to the estimated linear model, if the value of the independent variable is increased by one unit, then the change in the dependent variable yˆy^ is given by?
Determine the value of the dependent variable yˆy^ at x=0x=0.
Determine if the statement "All points predicted by the linear model fall on the same line" is true or false.
Find the value of the coefficient of determination. Round your answer to three decimal places.
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