You know that there is a strong correlation between the consumption of ice cream and body weight. The Pearson's r = 0.78. You also know that the average consumption of ice cream per week is five grams with a standard deviation of 1.5 grams. The average weight is 65 kg with a standard deviation of 15 kg. What is the formula of the regression line?1 pointŷ = 26 + 7.8x ŷ = 7.8 + 26xŷ = -502 + 0.078x ŷ = 0.078 - 502x
Question
You know that there is a strong correlation between the consumption of ice cream and body weight. The Pearson's r = 0.78. You also know that the average consumption of ice cream per week is five grams with a standard deviation of 1.5 grams. The average weight is 65 kg with a standard deviation of 15 kg. What is the formula of the regression line?1 pointŷ = 26 + 7.8x ŷ = 7.8 + 26xŷ = -502 + 0.078x ŷ = 0.078 - 502x
Solution
The formula for a regression line is given by ŷ = a + bx, where:
- ŷ is the predicted value of the dependent variable (in this case, body weight)
- a is the y-intercept
- b is the slope of the line
- x is the value of the independent variable (in this case, ice cream consumption)
The slope (b) is calculated as (r * (sd_y / sd_x)), where r is Pearson's correlation coefficient, sd_y is the standard deviation of the dependent variable, and sd_x is the standard deviation of the independent variable.
So, b = 0.78 * (15 / 1.5) = 7.8
The y-intercept (a) is calculated as (mean_y - b * mean_x), where mean_y is the mean of the dependent variable and mean_x is the mean of the independent variable.
So, a = 65 - 7.8 * 5 = 26
Therefore, the formula of the regression line is ŷ = 26 + 7.8x.
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