1 A simple linear regression equation relates Vand S as foll

1. A simple linear regression equation relates Vand S as follows a. The dependent variable is and the explanatory variable is b. The intercept parameter is c. Vis equal to a when S is equal to d. For each one-unit increase in S, the change in Vis and the slope parameter is. units 2. Twenty-eight data points on F and M are employed to estimate the parameters in the linear relation F-a bM. The computer output from the regression analysis is the following PVALUE ON 0.0001 DEPENDENT VARIABLE: F R-SQUARE F-RATIO OBSERVATIONS: 28 0.6449 47.215 PARAMETER STANDARD ESTIMATE 350.00 VARIABLE ERROR T-RATIO P-VALUE 0.0008 0.0039 3.79 92.330 4.650 INTERCEPT 14.75 What is the equation of the sample regression line? Test the intercept and slope estimates for statistical significance at the 1 percent significance level. Explain how you performed this test, and present your results Interpret the p-values for the parameter estimates. a. b. c. d. Test the overall equation for statistical significance at the 5 percent significance level Explain how you performed this test, and present your results. Interpret the p-value for the F-statistic If M equals 25, what is the fitted (or predicted) value of Y? What fraction of the total variation in Fis explained by the regression? e.

Solution

As per rules I will answer the first 4 subparts of the question.

1a:V , S

(V is dependent variable since its value depends upon the other variables. S is explanatory variable since it determines the value of V)

1b: a,b

(a is the intercept. It is the constant and is the point at which the line crosses the Y axis. B is the slope. It represents the change in V over the change in S.It indicates the direction of the line)

1c:0

When S=0, the equation will be V=a+b*0 and hence V=a.

1d:b

When there is a 1 unit increase in S,V will increase by b units. For example V= a+ b*1, V has increase by b units. If S increases by 1 more unit, V= a+ b*2, again V will increase by b units.