Problem 1
The dependent variable is assumed to be values of a land.
a) Use the Excel regression tool to do the linear regression,and provide the
“Line Fit Plots†(which is provided in the regressioninterface). (5 points)
b) What can the plot tell you? E.g., does it show that thefitting is good?
(5 points)
c) Now check the output.
c.1) What is the standard error of the estimate of the slope? (5points)
c.2) What is the t-test statistic for the slope? Reproduce thet-test statistic
in Excel using other values in the output (e.g., point estimateand standard
error). (10 points)
c.2) What is the 95% confidence interval of the slope? Reproducethe con-
fidence interval in Excel using other values in the output(e.g., t stat). Can
we use the confidence interval to claim that the independentvariable can be
dropped in the linear regression model? (10 points)
c.3) What is the p-value for the estimate of the slope?Reproduce the p-value
in Excel using other values in the output (e.g., t stat). Can weuse the p-values
to claim that the independent variable can be dropped in thelinear regression
model? (10 points)
c.4) Does the linear regression model fit well? Explain youranswer. (5
points)
d) Assume that the area of the land you are considering to sellis only one
acre. Does the linear regression model provide a good predictionfor the value
of your land? (5 points)
e) Assume that you want to check if the slope should besignificantly bigger
than 10,000.
e.1) Write the hypotheses. (5 points)
e.2) What is the new t-test statistic? (5 points)
e.3) What is the new p-value for the estimate of the slope? Isthe slope
significantly bigger than 10,000? (10 points)
| Values |
| 836,586,000 |
| 986,547,000 |
| 1,075,609,000 |
| 381,443,000 |
| 889,148,000 |
| 1,096,422,000 |
| 1,340,628,000 |
| 903,129,000 |
| 785,261,000 |
| 1,407,381,000 |
| 799,722,000 |
| 1,242,590,000 |
| 378,638,000 |
| 395,110,000 |
| 582,299,000 |
| 286,805,000 |
| 1,286,312,000 |
| 188,313,000 |
| 529,053,000 |
| 700,357,000 |
| 1,123,597,000 |
| 392,277,000 |
| 1,068,679,000 |
| 576,348,000 |
| 535,527,000 |
| 797,064,000 |
| 854,322,000 |
| 1,415,763,000 |
| 1,110,576,000 |
| 543,485,000 |
| 621,503,000 |
| 44,632,000 |
| 473,953,000 |
| 129,286,000 |
| 372,399,000 |
| 604,300,000 |
| 432,818,000 |
| 748,532,000 |
| 139,826,000 |
| 456,433,000 |
| 1,694,543,000 |
| 967,926,000 |
| 1,009,765,000 |
| 1,085,302,000 |
| 1,089,378,000 |
| 1,331,657,000 |
| 364,124,000 |
| 1,070,730,000 |
| 1,536,796,000 |
| 1,426,503,000 |
| 796,188,000 |
| 1,559,685,000 |
| 493,466,000 |
| 743,640,000 |
| 376,926,000 |
| 957,234,000 |
| 169,340,000 |
| 157,625,000 |
| 309,507,000 |
| 265,410,000 |
| 251,621,000 |
| 412,789,000 |
| 136,533,000 |
| 184,032,000 |
| 256,578,000 |
| 228,716,000 |
| 565,330,000 |
| 219,363,000 |
| 388,716,000 |
| 81,059,000 |
| 371,794,000 |
| 853,684,000 |
| 618,448,000 |
| 1,032,717,000 |
| 876,501,000 |
| 157,428,000 |
| 726,993,000 |
| 1,178,550,000 |
| 762,332,000 |
| 1,269,773,000 |
| 1,018,473,000 |
| 895,709,000 |
| 2,412,768,000 |
| 1,211,090,000 |
| 1,060,153,000 |
| 2,145,334,000 |
| 1,050,692,000 |
| 1,227,843,000 |
