A linear model has a design matrix that is a 66×7 matrix. Calculate the average leverage to two decimal places.
时间: 2024-05-24 10:14:58 浏览: 15
The average leverage for a linear model with design matrix X is given by the formula:
$avg.\; leverage = \frac{p}{n}$
where p is the number of columns in X (i.e., the number of parameters in the model) and n is the number of rows in X (i.e., the number of observations).
In this case, p = 7 and n = 66, so:
$avg.\; leverage = \frac{7}{66} \approx 0.11$
Therefore, the average leverage for this linear model is approximately 0.11, rounded to two decimal places.
相关问题
Design a Python APP that can calculate the precise value of pi to 1000 decimal places
我可以回答这个问题。可以使用Python中的decimal模块来计算pi的值,代码如下:
```python
from decimal import *
getcontext().prec = 100
pi = Decimal()
k =
while True:
pi += (Decimal(1)/(16**k))*((Decimal(4)/(8*k+1))-(Decimal(2)/(8*k+4))-(Decimal(1)/(8*k+5))-(Decimal(1)/(8*k+6)))
k += 1
if k > 100:
break
print(pi)
```
这个程序将计算pi的值并输出到100位小数。
A decision tree has 21 21 internal nodes including the root. Calculate the number of leaves of the tree.
Let us assume that the decision tree has L leaf nodes.
We know that the total number of nodes in a decision tree is given by the formula:
N = I + L
where N is the total number of nodes, I is the number of internal nodes and L is the number of leaf nodes.
In this case, we are given that the decision tree has 21 internal nodes (including the root). Therefore, we can substitute the given values in the above formula to get:
N = I + L
N = 21 + L
Now, we need to find the value of L. For this, we can use the fact that each internal node in a decision tree has at least two child nodes. Therefore, we can write:
I = 2^(h-1)
where h is the height of the tree. Since the root node is included in the count of internal nodes, we have:
h = height of the tree = number of levels - 1.
Let us assume that the decision tree has d levels. Then, we can write:
d = h + 1
Substituting the value of h in the equation for I, we get:
I = 2^(d-2)
Now, we can substitute the given value of I in the equation for N to get:
N = I + L
21 + L = 2^(d-2) + L
Simplifying this equation, we get:
2^(d-2) = 21
Taking the logarithm of both sides, we get:
d-2 = log2(21)
d = log2(21) + 2
d ≈ 5.45
Since the height of the tree is a whole number, we can round up the value of d to 6. Therefore, the decision tree has 6 levels.
Now, we can use the formula for the total number of nodes to find the number of leaf nodes:
N = I + L
21 + L = 2^(6-2) + L
21 + L = 16 + L
L = 5
Therefore, the decision tree has 5 leaf nodes.