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, you need to use the formula:

Se(b1) = sqrt( [ (SSE / (n-2)) / ((x - x̄)^2) ], where SSE represents the sum of squared errors, n is the sample size, x is the independent variable, and x̄ is the mean of x.

1. Calculate the SSE. To do this, you need some additional information, such as the actual values of y and x. The SSE is calculated as:

SSE = Σ (y - ŷ)^2, where Σ is the summation symbol, y represents the actual values of the dependent variable, and ŷ is the predicted values of the dependent variable (obtained by substituting the x values into the regression equation).

2. Once you have SSE, calculate Se(b1) using the formula mentioned earlier.

To find the corresponding t-statistic, use the formula:

t = (b1 - 0) / Se(b1), where b1 is the estimated coefficient for x in the regression equation (in this case, 100), and Se(b1) is the estimated standard deviation of b1.

a) For the null and alternative hypotheses:

Null hypothesis (Ho): b1 = 0
Alternative hypothesis (Ha): b1 ≠ 0 (two-tailed test)

To determine if you can reject the null hypothesis at the 1% level of significance, you need to compare the calculated t-statistic with the critical t-value.

Look up the critical t-value in a t-distribution table or use statistical software. Determine the degrees of freedom, which is equal to n - 2 (in this case, the sample size minus 2). For a 1% level of significance and a two-tailed test, you need to find the critical t-value such that the area in each tail is 0.5% (0.01 / 2 = 0.005). Compare the calculated t-statistic with the critical t-value.

If the absolute value of the calculated t-statistic is greater than the critical t-value, you can reject the null hypothesis and conclude that there is a significant relationship between the independent variable (x) and the dependent variable (y).

b) To find the F-statistic, you need to first calculate the mean sum of squares (MSSR) and the mean sum of squares of error (MSE).

MSSR = SSR / dfR, where SSR represents the sum of squares regression and dfR is the degrees of freedom for regression (equal to the number of independent variables, which is 1 in this case).

MSE = SSE / dfE, where dfE is the degrees of freedom for error (equal to n - k - 1, where k is the number of independent variables).

Then, calculate the F-statistic using the formula:

F = MSSR / MSE

For the null and alternative hypotheses:

Null hypothesis (Ho): All coefficients are equal to zero (b1 = b0 = 0)
Alternative hypothesis (Ha): At least one coefficient is not equal to zero (b1 ≠ 0 or b0 ≠ 0 or both)

To determine if the equation is significant at the 1% level using the p-value approach, you need to compare the calculated F-statistic with the critical F-value. Look up the critical F-value in an F-distribution table or use statistical software.

If the calculated F-statistic is greater than the critical F-value, you can reject the null hypothesis and conclude that the equation is significant at the 1% level.