Answer: First option is correct.
Explanation:
Since we have given that
![y=2x+1.5](https://img.qammunity.org/2019/formulas/mathematics/high-school/xser9r1n0eq837fycrt5ihp3cvf1rev4yb.png)
If the point (1,4) is in the data set.
we need to find the residual of 1.
At x = 1,
![y=2x+1.5\\\\y=2* 1+1.5\\\\y=2+1.5\\\\y=3.5](https://img.qammunity.org/2019/formulas/mathematics/high-school/khh85n7r7ug3lom1x9pmt0437yivey6vr7.png)
So, At x = 1, the value of y = 3.5
As we know that
![Residual\ value=Estimate\ value-Actual\ value\\\\Residual\ value=4-3.5\\\\Residual\ value=0.5](https://img.qammunity.org/2019/formulas/mathematics/high-school/p8rgyx5uo9ubon07r940pp11gl9s4y2yz1.png)
Hence, The residual of 1 is 0.5.
Thus, First option is correct.