I need help with this problem. Please take me step by step so I understand. Than
ID: 3055265 • Letter: I
Question
I need help with this problem. Please take me step by step so I understand. Thank you.
Age of Cars (years) Mileage
1.00 40.00
1.00 25.00
2.00 37.00
2.00 35.00
3.00 36.00
3.00 35.00
4.00 32.00
5.00 30.00
6.00 25.00
10.00 20.00
Mean of X=3.7
Mean of Y= 31.5
Sd of X=2.75
Sd of Y= 6.38
covxy= -12.83
1)What is the difference between the predicted and observed value for Mileage when a car is 4 years old?
2)Calculate and interpret ?. Is the effect significant? Why or why not?
3)Calculate and interpret r2.
Explanation / Answer
1)
calculation of slope and intercept manually
y^ = a + b *x
b = Cov(X,Y)/Var(X)
= -12.83/2.75^2
= -1.69652
a = ybar - b *xbar
= 31.5 + 1.69652*3.7
= 37.777124
y^ = 37.777124 -1.69652* x
now for x = 4
y^ = 37.777124 -1.69652* 4
=30.991044
difference = yi - y^ = 32 -30.991044
=1.008956
using regression in excel
2) i assume ? is slope .
slope = -1.696035
it means when age is increased by 1 year , the mileage is decreased by 1.696 units.
p-value = 0.01629 < 0.05
hence it is significant
3)
R^2 = 0.53449
it means 53.449 % of variability in mileage is explained by this model
Please rate
SUMMARY OUTPUT Regression Statistics Multiple R 0.731091002 R Square 0.534494053 Adjusted R Square 0.47630581 Standard Error 4.618007275 Observations 10 ANOVA df SS MS F Significance F Regression 1 195.8920705 195.8920705 9.185602148 0.016290181 Residual 8 170.6079295 21.32599119 Total 9 366.5 Coefficients Standard Error t Stat P-value Lower 95% Intercept 37.7753304 2.533716311 14.90906075 4.03941E-07 31.93257011 X Variable 1 -1.696035242 0.559604318 -3.030775833 0.016290181 -2.986485113