Check and develop my answers, multiple regression

#1
This is the question, i was wondering if anyone could check if i did the correct thing, and help me develop my written answers if needed.




a) For every 0.08 change in X, y will change by one. Also Rsquared is 0.43 which means 43% of changes in Y can be explained by the variable X.

- What else can i add to this?

b) Test statistic t=b1/sb1

= 0.08/0.012 = 6.66. With n=70 this is 70 deg of freedom, looknig at t distrbution table we are givem, i have to use the value of 80, this gives a 95% confidence value of 1.99

Since 6.66 > 1.99 this means it is significant.

What else can i say about this?

c) F statitistic = (N-2)Rsquared/ (1-Rsquared)

= (70-2) 0.43 / ( 1-0.43) = 29.24/0.57 = 51.29

I know i have to comapre this to a critical value, and if its bigger then its significant and it backs up T, however i dont know which value to look at on an F table.

Also when i do have that value what can i explain further?


Thanks will be given to all suggestions and help :)
 

vinux

Dark Knight
#2
a) For every 0.08 change in X, y will change by one. Also Rsquared is 0.43 which means 43% of changes in Y can be explained by the variable X.

- What else can i add to this?
I think you were bit careless in the interpretation.It should be
For every unit(1) change in X, Y will change by 0.08.

And it is better if you replace X & Y by actual variable

b) Test statistic t=b1/sb1

= 0.08/0.012 = 6.66. With n=70 this is 70 deg of freedom, looknig at t distrbution table we are givem, i have to use the value of 80, this gives a 95% confidence value of 1.99

Since 6.66 > 1.99 this means it is significant.

What else can i say about this?
It seems correct. I guess 0.012 is the standard deviation. But I think the table tvalue is 1.96( for you it is 1.99)

c) F statitistic = (N-2)Rsquared/ (1-Rsquared)

= (70-2) 0.43 / ( 1-0.43) = 29.24/0.57 = 51.29

I know i have to comapre this to a critical value, and if its bigger then its significant and it backs up T, however i dont know which value to look at on an F table.

Also when i do have that value what can i explain further?
Formula is correct. F-tables are available in the net. see the link below
http://www.statsoft.com/textbook/sttable.html

here numerator (df1 ) df will be 1 and denominator df will be 70-2 = 68 and in this case table F value approx 2.8
 
#3
thanks for helping, but could you explain further how i get this F value, what table am i looking at and how do i read down and across, as im still a little unsure :)

thanks again
 

vinux

Dark Knight
#4
thanks for helping, but could you explain further how i get this F value, what table am i looking at and how do i read down and across, as im still a little unsure :)

thanks again
Sorry!. In your case table F value will be 3.982 ( 2.8 is the table F value for alpha =.10)
df1 = no. parameters in the model -1 = 2-1 =1
df2 = 70-2 = 68. df1 column index and df2 raw index.

From the Table (F Table for alpha=.05) you can find F(1,60) and F(1,120).
F(1,60) = 4.0012 & F(1,120)=3.9201
So F(1,68) will be between value of above.

For detailed table see the link below
http://www.itl.nist.gov/div898/handbook/eda/section3/eda3673.htm
 
#5
Ah right iget it now cheers :)

so because the F stat worked out is greater than the critical value, that means it is significant, and it backs up the T statistic which i also proved to be significant :)