Wood scientists are interested in replacing solid-wood building material by less expensive products made from wood flakes. Some summary statistics obtained from a study of the relationship between the length (in inches) and the strength (in pounds per square inch) of beams made from wood flakes. The scatterplot of Length versus Strength was approximately linear. We want to predict strength based on length.
Mean length = 9.500
Mean strength = 291.3
Standard Deviation length= 3.028
Standard Deviation strength = 71.2
Minimum length = 5.000
Minimum strength = 234.0
Q1 length = 6.750
Q1 strength= 242.8
Median length = 9.500
Median strength = 251.5
Q3 length= 12.250
Q3 strength = 343.3
What is the regression equation?
b1= r sy/sx= -0.882 ( 71.2/3.028)=-20.739
b0= y - b1x = 291.3 - (-20.739x 9.500)= 488.322
y= 488.322-20.739
Im getting the wrong answer
There is a calculation error for b0. It should be 488.323
Therefore, Y=488.323+(-20.739)*x
To find the regression equation, you need to use the formula:
y = b0 + b1x
where y represents the predicted strength, x represents the length, b0 is the intercept, and b1 is the slope.
To calculate the slope (b1), you can use the formula:
b1 = r * (sy / sx)
where r is the correlation coefficient, sy is the standard deviation of the strength, and sx is the standard deviation of the length.
In your case, the calculated b1 value is incorrect. The correct calculation would be:
b1 = -0.882 * (71.2 / 3.028) = -20.736
So the correct value for b1 is -20.736 (you rounded it to -20.739 in your calculation).
Next, you can use the mean length and mean strength values along with the b1 value to calculate the intercept (b0):
b0 = y - b1x
b0 = 291.3 - (-20.736 * 9.5) = 291.3 + 196.944 = 488.244
So the correct value for b0 is 488.244 (you rounded it to 488.322 in your calculation).
Finally, you can write the regression equation as:
y = 488.244 - 20.736x
Make sure to use the correct values for b1 and b0 in your calculation to get the correct regression equation.