Question

In: Statistics and Probability

y x1 x2 x3 College Ranking Annual Cost Admission Rate 4Yrs Grad. 98 $37,330 84 66...

y x1 x2 x3
College Ranking Annual Cost Admission Rate 4Yrs Grad.
98 $37,330 84 66
143 $44,570 82 70
153 $54,464 85 72
193 $35,074 29 41
198 $33,160 89 45
201 $46,852 76 63
208 $24,053 82 42
224 $48,068 76 64
229 $40,788 78 62
256 $54,148 85 65
258 $34,745 82 54
261 $25,309 86 34
269 $29,328 81 40
279 $35,934 85 38
286 $49,060 83 61
293 $40,730 97 49
299 $31,908 22 20
302 $32,310 77 26
303 $37,322 78 47
304 $38,654 81 44
305 $27,152 86 36
310 $43,355 76 54
314 $49,608 84 52
319 $47,630 79 61
334 $47,090 92 59
339 $40,958 78 54
340 $43,868 83 50
355 $42,896 77 45
356 $27,445 83 36
357 $49,587 76

52

1. Run Multiple Regression for X1X2X3 Write regression equation and coefficient of determination.Explain equation and r squared.

2. Write equation and coefficient of determination, then select 3 sets of numbers and predict the values of Y. (Remember the range.)

3. Calculate +-1, +-2, and +-3 standard deviations from the mean (Use Descriptive Statistics.), Identify outliers and discuss F significance

Solutions

Expert Solution

We will be applying the Linear regression model here, it can be done by using the function LINEST(y_value, x_value, TRUE, TRUE) where y_values contain values of y here and x_values have x1, x2, x3 values.

Select 5 rows and 4 columns and then write the formula in the first cell and after that, press Shift + Ctrl + Enter.    

The equation comes out to be-

y = 180.1385 + 0.007*x1 + 1.72*x2 - 6.55*x3  

Coefficient of determination(R**2) comes out to be 0.5465, which means change in y can be 54.65% explained by x1, x2 and x3.

Taken 3 values of x1, x2, and x3 and predicted y here -

x1 x2 x3 y(predicted) y
24053 82 42 216.804649 208
48068 76 64 233.01582 224
40788 78 62 197.818698 229

y predicted was calculated like this -

y(predicted) = 180.1385+(0.007107*L6)+(1.718549*M6)-(6.55237*N6)  

mean 269.5333
S.D 67.31743
mean + S.D 336.8508
mean - S.D 202.2159
mean + 2*S.D 404.1682
mean - 2*S.D 134.8985
mean + 3*S.D 471.4856
mean - 3*S.D 67.58103

orchestra answered 1 year ago
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