The accompanying data are the length (in centimeters) and girths (in centimeters) of 12 harbor seals. Find the equation of the regression line. Then construct a scatter plot of the data and draw the regression line. Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. If the x-value is not meaningful to predict the value of y, explain why not. (a) x=140 cm (b) x=172 cm (c) x=164 cm (d) x=158 cm Length, x Girth, y 137 107 168 130 153 117 146 106 160 124 160 120 123 103 137 104 155 119 148 111 146 107 145 110 (a) The equation of the regression line is y= x+ . (Round to two decimal places as needed.) Construct a scatter plot of the data and draw the regression line. Plot length on the horizontal axis and girth on the vertical axis. (b) Predict the girth for a length of 140 cm, if it is meaningful. Select the correct choice below and, if necessary, fill in the answer box within your choice. Fill for y if necessary A. y= cm (Round to two decimal places as needed.) B. It is not meaningful to predict this value of y because x=140 is inside the range of the original data. C. It is not meaningful to predict this value of y because x=140 is not an x-value in the original data. (c) Predict the girth for a length of 172 cm, if it is meaningful. Select the correct choice below and, if necessary, fill in the answer box within your choice. fill Y if necessary A. y= cm (Round to two decimal places as needed.) B. It is not meaningful to predict this value of y because x=172 is well outside the range of the original data. C. It is not meaningful to predict this value of y because x=172 is not an x-value in the original data. (d) Predict the girth for a length of 164 cm, if it is meaningful. Select the correct choice below and, if necessary, fill in the answer box within your choice. fill for y if necessary A. y=nothing cm (Round to two decimal places as needed.) B. It is not meaningful to predict this value of y because x=164 is not an x-value in the original data. C. It is not meaningful to predict this value of y because x=164 is inside the range of the original data. (e) Predict the girth for a length of 158 cm, if it is meaningful. Select the correct choice below and, if necessary, fill in the answer box within your choice. Fill for Y if necessary A. y= cm (Round to two decimal places as needed.) B. It is not meaningful to predict this value of y because x=158 is inside the range of the original data. C. It is not meaningful to predict this value of y because x=158 is not an x-value in the original data
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)
x=140
cm |
(b)
x=172
cm |
(c)
x=164
cm |
(d)
x=158
cm |
Length, x Girth, y
137 107
168 130
153 117
146 106
160 124
160 120
123 103
137 104
155 119
148 111
146 107
145 110
Construct a scatter plot of the data and draw the regression line. Plot length on the horizontal axis and girth on the vertical axis.
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