Question

People in the aerospace industry believe the cost of a space project is a function of the weight of the major object being sent into space. You will use the following data to develop a regression model to predict the cost of a space project by the weight of the space object. Object Weight (tons) 1. 1.897, 2. 3.019, 3. 0.453 , 4. 0.988, 5. 1.058, 6. 2.100, 7. 2.387 total 11.902

Project Cost ($millions) 1. 53.6, 2. 184.9 ,3. 6.4, 4. 23.5, 5. 33.4, 6. 110.4, 7. 104.6, Totals: 516.8

a. Complete all of the blank entries in the partial Excel output below.

Regression Statistics

Multiple R

R Square

Standard Error

Observations.

ANOVA SS DF MS F

REGRESSION

RESIDUAL 446.4700921   

TOTAL 23744.45429

COEFFCIENTS STANDARD ERROR T STAT

INTERCEPTS -39.00709075 18.1114242

WEIGHTS(TONS) 9.560469477 6.941370994

b.Calculate the least squares regression equation for predicting the cost of a space project as a function of the weight of the major object being sent into space.

c. Interpret the practical meaning of the slope of the least squares regression line (i.e., in the context of the problem, in plain English).

d. Identify the independent and dependent variables in this regression analysis.

e. Using a significance level of ? = .05, is there sufficient evidence to conclude that the weight of the major object being sent into space is useful in predicting the cost of a space project? Do a complete and appropriate hypothesis test.

f. What proportion of the total variability in the cost of a space project can be explained by knowing the weight of the major object being sent into space?

g. Calculate the coefficient of correlation between the independent and dependent variables. Comment on what the magnitude and direction of this correlation coefficient says about the linear relationship between the independent and dependent variable.

h. Construct an appropriate interval estimate of the mean cost of all space projects when the weight of the major object being sent into space is 1.5 tons, with 95% confidence. Interpret the practical meaning of this interval estimate, in plain English.

i. Construct an appropriate interval estimate of the cost of a single space project when the weight of the object being sent into space is 1.5 tons, with 95% confidence. Interpret the practical meaning of this interval estimate, in plain English.

j. Construct a 95% confidence interval estimate of the true population slope for this least squares regression line. Interpret the practical meaning of your interval estimate, in plain English.

k. Calculate and report the estimated variance of the random errors, ?, for this regression analysis.

l. Calculate and report the estimated standard deviation of the random errors, ?, for this regression analysis. m. Calculate and report the residual for the 2nd observation in the data set

Answer 1

a) i have attached an image containing all the required values and R program for calculating those values. Refer to the image for the answer of this part.

b) let weight be x and total project cost be y.Then, the least squares regression equation for predicting the cost of a space project as a function of the weight of the major object being sent into space is given by: y=a+bx

Where the coefficients a is given by a=mean of y-b*mean of x

And b=Covariance between x and y/variance of x

b=46.30846/0.814 09=56.88237

a=73.82857-(56.88237)*1.700286

=-22.8877

So, the required equation is given by :

Space project cost=-22. 8877+56.88237*weight of the object sent into space

C) slope of the regression line tells us the amount by which the response variable changes(increase or decreases) on average, when the explanatory variable changes by one.

Here, on changing the weight by one unit, the cost of space project is increasing by 56.8824 units.

D) here, cost of space project is dependent variable and weight of major objects sent into space is independent variable.

E) We know that if the p value for F test is less than significance level, tgen our sample provide sufficient evidence to conclude that our regression model fits the data better than the model with no independendent variable.

Here, we got p value as 0.0009529 which is less than significance level 0.05.hence there is evidence that weight of the major objects sent into space (which is independent variable) is useful in predicting the cost of space project.

F) We know that, COEFFICIENT of determination r² tells the measure of variability in response variable that is explained by explanatory variable.

Here R² is 0.906

So.90% of the variability in cost of space project can be explained by weight of the major objects sent into space.

G) correlation between the two variables is 0.9518

Which indicates a strong linear relationship between two i.e. With the increase in one variable, the variable will also increase.