Question

All logs are to base e

Size is in cubic centimeters, Age is in years, Weight is in pounds, Temperature is in degrees Fahrenheit, Height is in inches, Cost is in dollars, and Distance is in miles

The regression equation is
Log(Size) = 28.6 + 0.0292 Age - 1.124 Weight - 1.69 log(Temperature) + 1.02 log(Height) + 2.24 log(Cost) - 0.334 log(Distance)

Predictior	Coef	SE Coef	T	P
Constant	28.59	20.67	1.38	0.301
age	0.0292	0.083	12.27	0.006
weight	-1.124	0.052	-21.40	0.001
Log(temp)	-1.691	0.223	-7.58	0.002
Log(height)	1.0207	0.847	1.21	0.351
Log(cost)	2.239	0.42	5.06	0.004
Log(distance)	-0.334	0.0112	-2.98	0.049

S = 64.1788   R-Sq = 86.1%   R-Sq(adj) = 72.1%

Answer the following question using three decimals.
If the effect is not statistically significant put in NA
Put in percentages without the percent sign, so put in 10 instead of 10%

1-

As age increases by 1 year the size increases by the percentage

2 -

As weight increases by one pound the size decreases by the percentage

3-

As temperature increases by 7% the size will decrease by the percentage

4-

As Height increases by 3% the size increases by the percentage

5- As cost increases by 5% the size increases by the percentage

Answer 1

We know that the p-value for each term in regression model tests the null hypothesis that the coefficient is equal to zero (no effect). A low p-value (< 0.05) indicates that you can reject the null hypothesis.

And Here Null Hypothesis is : it is not statistically significant.

i.e. Conversely, a larger (insignificant) p-value suggests that changes in the predictor are not associated with changes in the response.

So here we see that in given example, p-value for Log(height) is larger than 0.05, So we accept the null hypothesis i.e. we conclude that, it is not statistically significant.. And we can see that the predictor variables of Age, Weight, Temp, Cost and Distance are significant because all of their p-values are less than 0.05.

1) As age increases by 1 year the size increases by 0.0292.

2) As weight increases by one pound the size decreases by 1.124.

3) As temperature increases by 7% the size will decrease by (1.69*log(7)) 1.4282%.

4) NA

5) As cost increases by 5% the size increases by (2.239*log(5)) 1.5651%.