Question

percent carbon weight supported (in kilograms)
1.03 1,066
1.11 1,186
1.18 1,123
1.23 1,102
1.30 1,208
1.48 1,265
1.69 1,194
1.71 1,301
the least squares regression line of this data set is:
y = 239.903x + 858.855
if a car frame is 1.15 percent carbon, how much weight does this line predict it can support?
round your answer to the nearest thousandth.
kilograms

Explanation:

Step1: Substitute \(x = 1.15\) into the regression equation

Given the regression line \(y=239.903x + 858.855\), substitute \(x = 1.15\)

$$y=239.903\times1.15+858.855$$

Step2: Calculate the product

$$239.903\times1.15 = 239.903\times(1 + 0.15)=239.903+239.903\times0.15$$

$$239.903\times0.15=(240 - 0.097)\times0.15=240\times0.15-0.097\times0.15 = 36- 0.01455=35.98545$$

$$239.903+35.98545 = 275.88845$$

Step3: Calculate the sum

$$y=275.88845+858.855$$

$$y = 1134.74345\approx1134.743$$

Answer:

\(1134.743\)