Day 9: Multiple Linear Regression

Objective
In this challenge, we practice using multiple linear regression. Check out the Tutorial tab for learning materials!

Task
Andrea has a simple equation:

for

real constants (

). We can say that the value of

depends on

features. Andrea studies this equation for

different feature sets

and records each respective value of

. If she has

new feature sets, can you help Andrea find the value of

for each of the sets?

Note: You are not expected to account for bias and variance trade-offs.

Input Format

The first line contains space-separated integers, (the number of observed features) and (the number of feature sets Andrea studied), respectively.
Each of the subsequent lines contain space-separated decimals; the first elements are features , and the last element is the value of for the line's feature set.
The next line contains a single integer, , denoting the number of feature sets Andrea wants to query for.
Each of the subsequent lines contains space-separated decimals describing the feature sets.

Constraints

Scoring
For each feature set in one test case, we will compute the following:

. We will permit up to a margin of error.

The normalized score for each test case will be: . If the challenge is worth points, then your score will be .

Output Format

For each of the feature sets, print the value of on a new line (i.e., you must print a total of lines).

Sample Input

2 7
0.18 0.89 109.85
1.0 0.26 155.72
0.92 0.11 137.66
0.07 0.37 76.17
0.85 0.16 139.75
0.99 0.41 162.6
0.87 0.47 151.77
4
0.49 0.18
0.57 0.83
0.56 0.64
0.76 0.18

Sample Output

Explanation

We're given , so . We're also given , so we determine that Andrea studied the following feature sets:

We use the information above to find the values of , , and . Then, we find the value of for each of the feature sets.