# Test the significance of the slope and y-intercept

Please, I need assistance building an excel doc, as well as detailed understanding of the placement, thank you.

Information:

A real estate agency collects data concerning y = the sales price of a house (in thousands of dollars), and x = the home size (in hundreds of square feet). The MINITAB output of a simple linear regression analysis of the data set for this case is given in table (below).

MINITAB Output of a Simple Linear Regression Analysis of the Real Estate Sales Price Data

The regression equation is

SPrice = 48.0 + 5.70 HomeSize

Predictor Coef SE Coef T P

Constant 48.02 14.41 3.33 0.010

HomeSize 5.7003 0.7457 7.64 0.000

S = 10.5880 R-Sq = 88.0% R-Sq(adj) = 86.5%

Analysis of Variance

Source DF SS MS F P

Regression 1 6550.7 6550.7 58.43 0.000

Residual Error 8 896.8 112.1

-------- ---------- ---------

Total 9 7447.5

Values of Predictors for New Observations

New Obs HomeSize

1 20.0

Predicted Values for New Observations

New Obs Fit SE Fit 95% CI 95% PI

1 162.03 3.47 (154.04, 170.02) (136.34, 187.72)

Real Estate Sales Price Data

Sales Price (y) Home Size (x)

180 23

98.1 11

173.1 20

136.5 17

141 15

165.9 21

193.5 24

127.8 13

163.5 19

172.5 25

(a) Find the least squares point estimates b0 and b1 of β0 and β1 on the output and report their values.(Round b0 to 2 decimal places and b1 to 4 decimal places.)

b0 ______

b1 ______

(b) Find SSE and s on the computer output and report their values. (Round SSE to 1 decimal place and s to 3 decimal places.)

SSE _______

s _______

(c) Find sb1 and the t statistic for testing the significance of the slope on the output and report their values. Show (within rounding) how t has been calculated by using b1 and sb1 from the computer output. (Round sb1 to 4 decimal places and t to 2 decimal places.)

sb1 _______

t _______

(d) Using the t statistic and appropriate critical value, test H0: β1 = 0 versus Ha: β1 ≠ 0 by setting α equal to .05. Is the slope (regression relationship) significant at the .05 level?

(Choose one) Reject / Do Not Reject not reject

H0. The slope is (Choose one) Not Significant / Significant at the .05 level.

(e Using the t statistic and appropriate critical value, test H0: β1 = 0 versus Ha: β1 ≠ 0 by setting α equal to .01. Is the slope (regression relationship) significant at the .01 level?

(Choose one) Do not reject / Reject

H0. The slope is (Choose one) Not Significant / Significant at the .01 level.

(f) Find the p-value for testing H0: β1 = 0 versus Ha: β1 ≠ 0 on the output and report its value. Using the p-value, determine whether we can reject H0 by setting α equal to .10, .05, .01, and .001. How much evidence is there that the slope (regression relationship) is significant? (Round your answer to 3 decimal places.)

p- value = _________ reject at (Choose one )

none

all α.

10 and .05

(g) Calculate the 95 percent confidence interval for β1 using numbers on the output. (Round your answers to 4 decimal places.)

[ ______ , ______ ]

(h) Calculate the 99 percent confidence interval for β1 using numbers on the output. (Round your answers to 3 decimal places.)

[ ______ , _______ ]

(i) Find sbo and the t statistic for testing the significance of the y intercept on the output and report their values. Show how t has been calculated by using b0 and sb0 from the computer output. (Round your answers to 2 decimal places.)

sb0 ___________________

t ___________________

(j) Find the p-value for testing H0: β0 = 0 versus Ha: β0 ≠ 0. Using the p-value, determine whether we can reject H0 by setting α equal to .10, .05, .01, and .001. What do you conclude about the significance of the y intercept? (Round your answer to 3 decimal places.)

p-value = __________

reject at (Choose one)

0.10 and 0.05, but not at 0.01 or 0.001

0.10 and but not at 0.05, 0.01 or 0.001

0.10, 0.05, and 0.01 but not at 0.001

None

(k) Using the appropriate data set and s from the computer output, hand calculate SSxx, sbo, and sb1. (Round your answers for SSxx to 1 decimal place and sb1 to 4 decimal places and sb0 to 2 decimal places.)

SSxx _________________

sb1 _________________

sbo _________________

https://brainmass.com/statistics/regression-model-validation/test-the-significance-of-the-slope-and-y-intercept-562256

#### Solution Summary

The solution contains detailed regression analysis performed on the given data and answers to the given questions.

Quantitative analysis questions a - l

The director of graduate studies at a large college of business would like to be able to predict the grade point index (GPI) of students in an MBA program based on Graduate Management Aptitude Test (GMAT) score. A sample of 20 students who had completed 2 years in the program is selected; the results are as follows:

[see the attached file for the table]

a. Plot a scatter diagram [Using Excel] and, assuming a linear relationship, use the least-squares method to find the regression coefficients b0 & b1.

b. Interpret the meaning of the Y intercept b0 and the slope b1 in this problem.

c. Use the regression equation developed in (a) to predict the GPI for a student with a GMAT score of 600.

d. Determine the standard error of the estimate.

e. Determine the coefficient of determination r² and interpret its meaning in this problem.

f. Determine the coefficient of correlation r.

g. Perform a residual analysis on your results and determine the adequacy of the fit of the model.

h. At the 0.05 level of significance, is there evidence of a linear relationship between GMAT score and GPI?

i. Set up a 95% confidence interval estimate for the average GPI of students with a GMAT score of 600.

j. Set up a 95% prediction interval for a particular student with a GMAT score of 600.

k. Set up a 95% confidence interval estimate of the population slope.

l. Suppose the GPIs of the 19th and 20th students were incorrectly entered. The GPI for student 19 should be 3.76, and the GPI for student 20 should be 3.88. Repeat (a) - (k) and compare the results with your original results.

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