12.22 A regression was performed using data on 16 randomly selected charities in 2003. The variables were Y = expenses (millions of dollars) and X = revenue (millions of dollars). (a)Write
the fitted regression equation. (b)Construct a 95 percent confidence interval for the slope.(c) Perform a right-tailed t test for zero slope at á = .05. State the hypotheses clearly. (d) Use Excel to find the p-value for the t statistic for the slope.
Charities
Variables coefficient std. error
Intercept 7.6425 10.0403
Revenue 0.9467 0.0936
Could you please show me how to do this one.. I need a full example of how to work this one.. Thanks
nbn
Certainly! Let's go step by step to answer each part of your question:
(a) To write the fitted regression equation, we use the formula:
Y = β0 + β1 * X
Where:
Y is the dependent variable (expenses)
X is the independent variable (revenue)
β0 is the intercept coefficient
β1 is the regression coefficient for X (revenue)
From the given information, the intercept coefficient (β0) is 7.6425, and the regression coefficient for revenue (β1) is 0.9467. Therefore, the fitted regression equation is:
Y = 7.6425 + 0.9467 * X
(b) To construct a 95 percent confidence interval for the slope, we need to use the standard error of the regression coefficient for revenue. From the given information, the standard error for revenue (std. error) is 0.0936.
The formula to calculate the confidence interval is:
CI = β1 ± t * SE(β1)
Where:
CI is the confidence interval
t is the critical value from the t-distribution table for the desired confidence level (95% confidence level = 1.96)
SE(β1) is the standard error of the regression coefficient for X (revenue)
Plugging the values into the formula, we get:
CI = 0.9467 ± 1.96 * 0.0936
Calculating the confidence interval, we have:
CI = (0.7638, 1.1296)