You want to find the linear relation between the number of X-ray machines purchased at one time and the cost per machine. You have the following data:X: Number of machines purchased 1 3 6 10 15Y: Cost per widget (in thousand rupees) 89 85 79 73 64Suppose the R² between X and Y is 0.87. Which of the following conclusions can you draw from this?The linear relation between X and Y is weak, and their correlation will be positive.The linear relation between X and Y is weak, and their correlation will be negative.The linear relation between X and Y is strong, and their correlation will be positive.The linear relation between X and Y is strong, and their correlation will be negative.
Question
You want to find the linear relation between the number of X-ray machines purchased at one time and the cost per machine. You have the following data:X: Number of machines purchased 1 3 6 10 15Y: Cost per widget (in thousand rupees) 89 85 79 73 64Suppose the R² between X and Y is 0.87. Which of the following conclusions can you draw from this?The linear relation between X and Y is weak, and their correlation will be positive.The linear relation between X and Y is weak, and their correlation will be negative.The linear relation between X and Y is strong, and their correlation will be positive.The linear relation between X and Y is strong, and their correlation will be negative.
Solution
The linear relation between X and Y is strong, and their correlation will be negative.
This conclusion is drawn based on the R² value given. R², or the coefficient of determination, is a statistical measure that explains the proportion of the variance for a dependent variable that's explained by an independent variable or variables in a regression model. If the R² of a model is 0.87, that means 87% of the variance in Y can be explained by X.
The negative correlation is inferred from the data given. As the number of machines purchased increases, the cost per machine decreases. This is a negative correlation because as one variable increases, the other decreases.
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