GATE 2024 IN – Question 50
A 20-psig pressure gauge gives the following readings. Its regression line is $y=0.04x+10.32$. The coefficient of determination $R^2$ is ______ (three decimal places).
| x | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| y (psig) | 10.3 | 10.5 | 10.4 | 10.5 | 10.5 |
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 0.450 to 0.550
Explanation
The mean is $\bar y=10.44$. The regression line predicts 10.36, 10.40, 10.44, 10.48, and 10.52. Compute $SSE=\sum(y_i-\hat y_i)^2=0.016$ and $SST=\sum(y_i-\bar y)^2=0.032$.
Thus $R^2=1-SSE/SST=1-0.016/0.032=\boxed{0.500}$.