The regression line for \( Y \) vs \( X \) is given by \( Y=0.82 X+59.1 \). The standard deviations for \( X \) and \( Y \) are 1.5 and 2.2 respectively. Suppose now we construct a regression line that uses \( Y \) to predict \( X \). The predicted average increase of \( X \) when \( Y \) is increased by 1 unit is (Give your answer correct to 2 decimal places.)

To find the predicted average increase of \( X \) when \( Y \) is increased by 1 unit, we need to use the regression line that uses \( Y \) to predict \( X \). Given the regression line for \( Y \) vs \( X \) is \( Y = 0.82X + 59.1 \), we can find the regression line for \( X \) vs \( Y \) by swapping the variables \( X \) and \( Y \) in the equation. The regression line for \( X \) vs \( Y \) is \( X = 0.82Y + 59.1 \). Now, we need to find the predicted average increase of \( X \) when \( Y \) is increased by 1 unit. This can be calculated by finding the change in \( X \) when \( Y \) changes by 1 unit. Let's calculate the change in \( X \) when \( Y \) changes by 1 unit. Calculate the value by following steps: - step0: Calculate: \(0.82\times 1\) - step1: Multiply: \(0.82\) The change in \( X \) when \( Y \) changes by 1 unit is 0.82 units. Therefore, the predicted average increase of \( X \) when \( Y \) is increased by 1 unit is 0.82 units.