a. The least squares estimate of βb0, βb1, and the estimated regression line is b. For this model, r 2 = 0.959. This means, that 95.9 percent of variation in the number of large pizzas consumed, is explained by linear regression on the number of students watching the game. (true or false) c. The 95% confidence interval for number of pizzas when x ∗ = 5, is (5.71, 8.49). This means one can state with 95 percent confidence that i. When 5 students watch games on several occasions, the average number of large pizzas consumed is between 5.71 and 8.49. ii. When 5 students watch a game, the number of large pizzas consumed is between 5.71 and 8.49. The 95% prediction interval for number of pizzas when x ∗ = 5, is (4.21, 9.99). This means one can state with 95 percent confidence that i. When 5 students watch games on several occasions, the average number of large pizzas consumed is between 4.21 and 9.99. ii. When 5 students watch a game, the number of large pizzas consumed is between 4.21 and 9.99.
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.
a. The least squares estimate of βb0, βb1, and the estimated regression line is
b. For this model, r 2 = 0.959. This means, that 95.9 percent of variation in the number of large pizzas consumed, is explained by linear regression on the number of students watching the game. (true or false)
c. The 95% confidence interval for number of pizzas when x ∗ = 5, is (5.71, 8.49). This means one can state with 95 percent confidence that
i. When 5 students watch games on several occasions, the average number of large pizzas consumed is between 5.71 and 8.49.
ii. When 5 students watch a game, the number of large pizzas consumed is between 5.71 and 8.49.
The 95% prediction interval for number of pizzas when x ∗ = 5, is (4.21, 9.99). This means one can state with 95 percent confidence that
i. When 5 students watch games on several occasions, the average number of large pizzas consumed is between 4.21 and 9.99.
ii. When 5 students watch a game, the number of large pizzas consumed is between 4.21 and 9.99.
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