If z=(x+y)ey and x=u2+v2 and y=u2−v2, find the following partial derivatives using the chain rule. Enter your answers as functio
1 answer:
Answer:
Step-by-step explanation:
Given the functions z=(x+y) and x=u²+v² and y=u²−v²
Using the composite derivative formula;
∂z/∂u= ∂z/∂x*∂x/∂u+∂z/∂y*∂y/∂u
∂z/∂u = y*2u + [(x+y)
+x
]*2u
∂z/∂u =y*2u + 2u[x
+y
+x
]
∂z/∂u = y*2u + 2u[2x
+y
]
<em>∂z/∂u = 2u[u²−v²]</em><em>+ 2u[2(u²+v²)</em>
<em>+y</em>
<em>]]</em>
∂z/∂v= ∂z/∂x*∂x/∂v+∂z/∂y*∂y/∂v
∂z/∂v = y*2v + [(x+y)
+x
]*-2v
∂z/∂v =y*2v -2v[x
+y
+x
]
∂z/∂v = y*2v -2v[2x
+y
]
<em>∂z/∂v = 2v[u²−v²]</em><em>-2v[2(u²+v²)</em>
<em>+y</em>
<em>]</em>
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Answer:
So on this case for the significance level assumed we see that
so then we can conclude that the result is NOT significant. And we don't have enough evidence to reject the null hypothesis.
So on this case is not appropiate say that :"the more we spend on advertising this product, the fewer units we sell" since the slope for this case is not significant.
Step-by-step explanation:
Let's suppose that we have the following linear model:
Where Y is the dependent variable and X the independent variable. represent the intercept and
the slope.
In order to estimate the coefficients we can use least squares procedure.
If we are interested in analyze if we have a significant relationship between the dependent and the independent variable we can use the following system of hypothesis:
Null Hypothesis:
Alternative hypothesis:
Or in other words we want to check is our slope is significant (X have an effect in the Y variable )
In order to conduct this test we are assuming the following conditions:
a) We have linear relationship between Y and X
b) We have the same probability distribution for the variable Y with the same deviation for each value of the independent variable
c) We assume that the Y values are independent and the distribution of Y is normal
The significance level assumed on this case is
The standard error for the slope is given by this formula:
Th degrees of freedom for a linear regression is given by since we need to estimate the value for the slope and the intercept.
In order to test the hypothesis the statistic is given by:
The p value on this case would be given by:
So on this case for the significance level assumed we see that
so then we can conclude that the result is NOT significant. And we don't have enough evidence to reject the null hypothesis.
So on this case is not appropiate say that :"the more we spend on advertising this product, the fewer units we sell" since the slope for this case is not significant.