consider b1=100 and b0=5, this gives us the estimated regression equation of y=100x+5
Find the estimated standard deviation of b1 and the corresponding t-statistic.
a.)At the 1% level of significance, can you reject the null hypothesis? Make sure you state
the null and alternative hypotheses.
b.)Find the F-statistic. Is the equation significant at the 1% level? Make sure you
state the null and alternative hypotheses. Use the p-value approach.
my answers:
a) Ho:b1=0
ha:b1 cant equal 0
not sure how to do the rest of the question, please help
To find the estimated standard deviation of b1, also known as the standard error of the slope, we can use the following formula:
SE(b1) = √[ (∑(y - ŷ)²) / ((n - 2) ∑(x - x̄)²)]
Where:
y = Actual y values
ŷ = Predicted y values
n = Number of observations
x = Independent variable
x̄ = Mean of x values
In this case, we have b1 = 100 and b0 = 5, so the estimated regression equation is y = 100x + 5. However, you haven't provided any x or y values, making it impossible to calculate the standard error of the slope.
Regarding the t-statistic, we can calculate it using the formula:
t = (b1 - 0) / SE(b1)
Where 0 is the value of the null hypothesis. In this case, the null hypothesis is Ho: b1 = 0.
Given that b1 is 100, you can substitute these values into the formula to find the t-statistic.
Now, let's proceed to answer your questions:
a) At the 1% level of significance, can you reject the null hypothesis? Make sure you state the null and alternative hypotheses.
The null hypothesis is Ho: b1 = 0, and the alternative hypothesis is Ha: b1 ≠ 0. To determine whether we can reject the null hypothesis at the 1% level of significance, we need to compare the calculated t-statistic to the critical value of the t-distribution.
To reject the null hypothesis, the t-statistic must have an absolute value greater than the critical value. You would need to look up the critical value for a two-tailed test at the 1% significance level, with the degrees of freedom equal to n - 2 (where n is the sample size). Then, compare it to the calculated t-statistic to make the decision.
b) Find the F-statistic. Is the equation significant at the 1% level? Make sure you state the null and alternative hypotheses. Use the p-value approach.
To find the F-statistic and determine the significance of the equation using the p-value approach, we need additional information such as the number of independent variables and the residual sum of squares. Without this information, it is not possible to calculate the F-statistic or evaluate its significance at the 1% level.
If you provide the missing information, I can help you calculate the F-statistic and interpret the results.
To find the estimated standard deviation of b1, you need to calculate the standard error of the coefficient estimate. The formula for the standard error of b1 is:
Standard Error of b1 = sqrt(Mean Squared Error / (n * Variance of x))
In this case, since b1 is 100, b0 is 5, and the regression equation is y = 100x + 5, we assume that the distribution of errors (residuals) is normally distributed with a mean of 0 and use the following formulas to calculate the Mean Squared Error and Variance of x:
Mean Squared Error (MSE) = Sum of Squared Residuals / (n - 2)
Variance of x = Sum of Squared Deviations from x-bar / (n - 1)
To calculate the Sum of Squared Residuals, you need the actual observed values of y and the predicted values of y. Without that information, it is not possible to calculate the estimated standard deviation of b1.
Regarding the corresponding t-statistic, it can be calculated by dividing the estimated coefficient (b1) by the estimated standard deviation of b1. Since we don't have the estimated standard deviation of b1, we cannot calculate the t-statistic either.
Similarly, to find the F-statistic and determine whether the equation is significant at the 1% level, we need the Sum of Squared Residuals, the Total Sum of Squares, and the degrees of freedom. Without these values, it is not possible to calculate the F-statistic or determine the significance of the equation.
In summary, to answer the remaining parts of the question, you would need the actual observed values of y, the predicted values of y, and the x values to calculate the necessary statistics.