The following figures show the age of lambs (in days) and their weight when weighed in the autumn. Age Weight Age Weight 135 39 120 33 125 37 133 36 130 38 123 34 129 38 126 35 121 34 130 39 125 35 126 38 137 38 140 41 129 36 132 40 121 34 137 44 137 41 137 43 The mean age is 129.65 days and the standard deviation is 6.18. The average weight is 37.65 kg and the standard deviation is 3.10. The correlation between age and weight is 0.86. a) Find an equal regression line for the age of the lambs and their weight. b) How much of the variability in weight can be explained by age? c) How much does the weight change in 30 days according to the regression analysis?
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 following figures show the age of lambs (in days) and their weight when weighed in the autumn.
| Age | Weight | Age | Weight |
| 135 | 39 | 120 | 33 |
| 125 | 37 | 133 | 36 |
| 130 | 38 | 123 | 34 |
| 129 | 38 | 126 | 35 |
| 121 | 34 | 130 | 39 |
| 125 | 35 | 126 | 38 |
| 137 | 38 | 140 | 41 |
| 129 | 36 | 132 | 40 |
| 121 | 34 | 137 | 44 |
| 137 | 41 | 137 | 43 |
The mean age is 129.65 days and the standard deviation is 6.18. The average weight is 37.65 kg and the standard deviation is 3.10. The
a) Find an equal regression line for the age of the lambs and their weight.
b) How much of the variability in weight can be explained by age?
c) How much does the weight change in 30 days according to the regression analysis?
d) Predict the weight of a lamb that is 136 days old and given a 95% confidence interval for the prediction, use se = 1.64.
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