I need help with the following part. i cant seem to get it as it\'s very hard to
ID: 3316544 • Letter: I
Question
I need help with the following part. i cant seem to get it as it's very hard to compute.
The table below shows the shipments (in millions of dollars) of consumer durables and nondurables in Canada. Is there a linear relationship between the shipments of durables and nondurables? In other words, if we know the value of nondurables shipped in any one year, can we predict the value of durables during that year? (Hint: Make the value of nondurables the independent variable.) According to the model, if at any given year the nondurables shipment is $212,000 million, what would the predicted amount for durables shipment be for the same year? Construct a confidence interval for the average y value for $212,000 million. Use the t statistic to test to determine whether the slope is significantl different from zero. Use = 0.05 Year 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 Nondurables $168,619 172,197 176,917 181,437 183,404 188,191 191,910 195,773 198,610 201,837 207,919 210,979 212,628 215,858 218,637 220,268 Durables $65,619 68,623 74,234 79,798 82,857 89,937 92,945 95,414 100,138 107,247 114,703 120,763 117,706 123,783 126,250 129,730 Source: Statistics Canada, CANSIM Table 380-0106, Gross domesticExplanation / Answer
Result:
r=0.9975
y = -148037.3757+1.258542 x
y predicted=118773
95% CI=(117628, 119919)
Observed t=53.07
Reject Ho.( coefficient is significant)
Regression Analysis
r²
0.9951
n
16
r
0.9975
k
1
Std. Error
1555.596
Dep. Var.
Durables
ANOVA table
Source
SS
df
MS
F
p-value
Regression
6,815,966,500.5356
1
6,815,966,500.5356
2816.66
0.0000
Residual
33,878,293.9019
14
2,419,878.1358
Total
6,849,844,794.4375
15
Regression output
confidence interval
variables
coefficients
std. error
t (df=14)
p-value
95% lower
95% upper
Intercept
-148,037.3757
4,677.7050
-31.647
0.0000
-158,070.0552
-138,004.6962
Nondurables
1.258542
0.0237
53.072
0.0000
1.2077
1.3094
Predicted values for: Durables
95% Confidence Interval
95% Prediction Interval
Nondurables
Predicted
lower
upper
lower
upper
Leverage
212,000
118,773.4507
117,628.3308
119,918.5707
115,245.986
122,300.915
0.118
Regression Analysis
r²
0.9951
n
16
r
0.9975
k
1
Std. Error
1555.596
Dep. Var.
Durables
ANOVA table
Source
SS
df
MS
F
p-value
Regression
6,815,966,500.5356
1
6,815,966,500.5356
2816.66
0.0000
Residual
33,878,293.9019
14
2,419,878.1358
Total
6,849,844,794.4375
15
Regression output
confidence interval
variables
coefficients
std. error
t (df=14)
p-value
95% lower
95% upper
Intercept
-148,037.3757
4,677.7050
-31.647
0.0000
-158,070.0552
-138,004.6962
Nondurables
1.258542
0.0237
53.072
0.0000
1.2077
1.3094
Predicted values for: Durables
95% Confidence Interval
95% Prediction Interval
Nondurables
Predicted
lower
upper
lower
upper
Leverage
212,000
118,773.4507
117,628.3308
119,918.5707
115,245.986
122,300.915
0.118