A linear model for a set of data was y = –20.6 + 9.72x and produced the following residual plot: [Xscl = 1, Yscl = 5]
Scatterplot
a) Predict the value of y when x = 7.5.
b) Determine the residual if x = 5. (2 points)
a) y = -20.6 + 9.72x
x = 7.5
y = -20.6 + 9.72(7.5) = 52.3
b) -6
thanks
To predict the value of y when x = 7.5, we can substitute x = 7.5 into the linear model equation y = -20.6 + 9.72x:
a) y = -20.6 + 9.72(7.5)
= -20.6 + 73.8
= 53.2
Therefore, the predicted value of y when x = 7.5 is 53.2.
To determine the residual if x = 5, we need to compare the actual value of y for x = 5 with the predicted value of y using the linear model equation:
b) Residual = Actual value of y - Predicted value of y
Let's say the actual value of y for x = 5 is y = 40. We can substitute the values into the equation:
Residual = 40 - (-20.6 + 9.72(5))
= 40 - (-20.6 + 48.6)
= 40 - 28
= 12
Therefore, the residual when x = 5 is 12.
To predict the value of y when x = 7.5, we can use the equation of the linear model, y = -20.6 + 9.72x.
a) To find the predicted value of y, substitute x = 7.5 into the equation:
y = -20.6 + 9.72(7.5)
Multiply 9.72 by 7.5:
y = -20.6 + 72.9
Add -20.6 to 72.9:
y = 52.3
Therefore, the predicted value of y when x = 7.5 is 52.3.
b) To determine the residual when x = 5, we need to compare the actual y-value at x = 5 with the predicted value from the linear model.
First, find the actual y-value at x = 5 either from the given data or the scatterplot.
Next, substitute x = 5 into the linear model and find the predicted value of y.
Then, subtract the actual y-value from the predicted value:
Residual = Predicted value - Actual value
Note: The residual measures the vertical difference between the actual data points and the regression line. It indicates how well the linear model fits the data points. A positive residual means the predicted value is greater than the actual value, while a negative residual means the predicted value is lower than the actual value.
Please provide the data or scatterplot for x = 5 to determine the actual y-value and compute the residual.