A plane is defined by two lines. What's the counterexample
1 answer:
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Answer:
a) For this case we can use the following R code to construct the qq plot
> data<-c(28.8, 24.4, 30.1, 25.6, 26.4, 23.9, 22.1, 22.5, 27.6, 28.1, 20.8, 27.7, 24.4, 25.1, 24.6, 26.3, 28.2, 22.2, 26.3, 24.4)
# The above line is in order to store the data in a vector
> qqnorm(data, pch = 1, frame = FALSE)
# The line above is in order to calculate the quantiles from the data assumin Normal distribution
> qqline(data, col = "steelblue", lwd = 2)
# The line above is in order to put a line for the theoretical dsitribution
The result is on the figure attached.
b) For this case as we can see on the figure attached the calculated quantiles are not far from the theorical quantiles given byt the straaigth blue line so then we can conclude that the distribution seems to be normal.
Step-by-step explanation:
For this case we have the following data:
28.8, 24.4, 30.1, 25.6, 26.4, 23.9, 22.1, 22.5, 27.6, 28.1, 20.8, 27.7, 24.4, 25.1, 24.6, 26.3, 28.2, 22.2, 26.3, 24.4
The quantile-quantile or q-q plot is a graphical procedure in order to check the validity of a distributional assumption for a data set. We just need to calculate "the theoretically expected value for each data point based on the distribution in question".
If the values are asusted to the assumed distribution, we will see that "the points on the q-q plot will fall approximately on a straight line"
For this case our distribution assumed is normal.
Part a
For this case we can use the following R code to construct the qq plot
> data<-c(28.8, 24.4, 30.1, 25.6, 26.4, 23.9, 22.1, 22.5, 27.6, 28.1, 20.8, 27.7, 24.4, 25.1, 24.6, 26.3, 28.2, 22.2, 26.3, 24.4)
# The above line is in order to store the data in a vector
> qqnorm(data, pch = 1, frame = FALSE)
# The line above is in order to calculate the quantiles from the data assuming Normal distribution (0,1)
> qqline(data, col = "steelblue", lwd = 2)
# The line above is in order to put a line for the theoretical distribution
The result is on the figure attached.
Part b
For this case as we can see on the figure attached the calculated quantiles are not far from the theorical quantiles given byt the straaigth blue line so then we can conclude that the distribution seems to be normal.
Answer:
y ≥ 8
Explanation:
Note that if f(x) is transformed into f(x + a) - b
The original functions is shifted a units to the left and b units downward.
Horizontal shifting will not affect the range of the function, only vertical shifting will change its range.
From the given, g(x) is the transformation of f(x) with
f(x) is shifted 2 units to the left and 3 units downward, we will disregard the horizontal shifting.
Since f(x) has a range of y ≥ 11, and g(x) is 3 units downward, the range will also move 3 units downward.
y ≥ 11 - 3
The answer is y ≥ 8