using excel data analysis tool for regression, following o/p is
obtained
Regression Statistics | ||||||
Multiple R | 0.9891 | |||||
R Square | 0.9783 | |||||
Adjusted R Square | 0.9759 | |||||
Standard Error | 10410.0972 | |||||
Observations | 11 | |||||
ANOVA | ||||||
df | SS | MS | F | Significance F | ||
Regression | 1 | 43995640108.01 | 43995640108 | 405.9757 | 0.0000 | |
Residual | 9 | 975331113.99 | 108370124 | |||
Total | 10 | 44970971222.00 | ||||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | |
Intercept | -3733948 | 193575.3942 | -19.2894 | 0.0000 | -4171846 | -3296050 |
X | 2000 | 99.2564 | 20.1488 | 0.0000 | 1775.367 | 2224.434 |
a)
so, answer is option b)
please note that option b) and option d) are same
b)
Ho: ß1= 0
H1: ß1╪ 0
n= 11
alpha= 0.01
SSxx = Σ(x-x̅)² = 11000.00
estimated std error of slope =Se(ß1) = Se/√Sxx = 10410/√11000 =
99.2564
t stat = ß1 /Se(ß1) =
20.149
t-critical value= 3.2498
since, t-stat > t-critical , reject Ho,
reject Ho and conclude that linear relations exists
between X and y
c)
p-value = 0.000 [using t table]
d)
decision : p-value<α , reject Ho
answer : option B)
e)
answer is No
f)
option c)
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