sychologist wants to determine if there is a linear relationship between the number of hours a person goes without sleep and the number of mistakes he/she makes on a simple test. The following data is recorded. Hours without sleep 32 38 48 24 46 35 30 34 42 Number of Mistakes 6 8 13 5 7 6 5 8 12 Hours without sleep=x, Number of mistakes=y (a) When you test the claim at the α = 0.01, that a linear relation exists between the two variables, find the critical value. Round critical value to nearest hundredth. (e.g. 0.135 would be entered as 0.14, -0.135 would be entered as -0.14, ± 0.135 would be entered as +/-0.14). (b) Find 95% confidence interval about the slope of the true lease-square regression line. Lower , Upper . Round confidence interval to nearest thousandth. e.g. 2.3457 would be entered as 2.346 (c) Based on question (b), does any linear relation exist between hours without sleep and number of mistakes? . (Enter yes or no, e.g. if you answer is "yes", enter as yes)
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.
Psychologist wants to determine if there is a linear relationship between the number of hours a person goes without sleep and the number of mistakes he/she makes on a simple test. The following data is recorded.
| Hours without sleep | 32 | 38 | 48 | 24 | 46 | 35 | 30 | 34 | 42 |
| Number of Mistakes | 6 | 8 | 13 | 5 | 7 | 6 | 5 | 8 | 12 |
Hours without sleep=x, Number of mistakes=y
(a) When you test the claim at the α = 0.01, that a linear relation exists between the two variables, find the critical value.
Round critical value to nearest hundredth. (e.g. 0.135 would be entered as 0.14, -0.135 would be entered as -0.14, ± 0.135 would be entered as +/-0.14).
(b) Find 95% confidence interval about the slope of the true lease-square regression line.
Lower , Upper . Round confidence interval to nearest thousandth. e.g. 2.3457 would be entered as 2.346
(c) Based on question (b), does any linear relation exist between hours without sleep and number of mistakes?
. (Enter yes or no, e.g. if you answer is "yes", enter as yes)
| x | y | x2 | y2 | xy | |
| 32 | 6 | 1024 | 36 | 192 | |
| 38 | 8 | 1444 | 64 | 304 | |
| 48 | 13 | 2304 | 169 | 624 | |
| 24 | 5 | 576 | 25 | 120 | |
| 46 | 7 | 2116 | 49 | 322 | |
| 35 | 6 | 1225 | 36 | 210 | |
| 30 | 5 | 900 | 25 | 150 | |
| 34 | 8 | 1156 | 64 | 272 | |
| 42 | 12 | 1764 | 144 | 504 | |
| 329 | 70 | 12509 | 612 | 2698 | Total |
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