The data shown below are the initial weights and gains in weight (in grams) of female rats on a high protein diet from 24 to 84 days of age. The point of interest in these data is whether the gain in weight is related to (dependent on) the initial weight. If so, then feeding experiments on female rats can be made more precise by adjusting for differences in initial weights of the rats. Statistically test this with a regression analysis.   Rat Number Initial Weight (gms) Weight Gain (gms) 1 50 128 2 64 159 3 76 158 4 64 119 5 74 133 6 60 112 7 69 96 8 68 126 9 56 132 10 48 118 11 57 107 12 59 106 13 46 82 14 45 103 15 65 104

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The data shown below are the initial weights and gains in weight (in grams) of female rats on a high protein diet from 24 to 84 days of age. The point of interest in these data is whether the gain in weight is related to (dependent on) the initial weight. If so, then feeding experiments on female rats can be made more precise by adjusting for differences in initial weights of the rats. Statistically test this with a regression analysis.

 

Rat Number Initial Weight (gms) Weight Gain (gms)
1 50 128
2 64 159
3 76 158
4 64 119
5 74 133
6 60 112
7 69 96
8 68 126
9 56 132
10 48 118
11 57 107
12 59 106
13 46 82
14 45 103
15 65 104

I used excel's regression took pak and got the following: 

SUMMARY OUTPUT              
                 
Regression Statistics              
Multiple R 0.489416452              
R Square 0.239528464              
Adjusted R Square 0.181030653              
Standard Error 8.869929833              
Observations 15              
                 
ANOVA                
  df SS MS F Significance F      
Regression 1 322.1498151 322.15 4.09466 0.064078516      
Residual 13 1022.783518 78.6757          
Total 14 1344.933333            
                 
  Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 33.30963866 13.41983835 2.48212 0.0275 4.317840516 62.3014368 4.317840516 62.3014368
Weight Gain (gms) 0.225101189 0.111242062 2.02353 0.06408 -0.01522267 0.46542505 -0.015222675 0.46542505

I do not know how to word Ho and Ha. Is the p and t values for weight gain or intercept?

***What is the equation for the multiple regression?

***What is the best estimate of the amount of variance in Y which is due to its regression on the independent variables?

 

 
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