Question

1.The following table gives mean daily calorie intake (all residents) and infant mortality rate (per 1000 births) for ten countries.

Country                Mean Daily Calories           Infant Mortality Rate

     Afghanistan                      1523                              154

             Austria                         3495                                 6

             Burundi                        1941                              114

            Colombia                       2678                               24

             Ethiopia                         1610                             107

            Germany                        3443                                6

              Liberia                          1640                             153

         New Zealand                     3362                                 7

             Turkey                          3429                               44

               USA                           3671                                 7

a)      Find the regression equation.

b)   Calculate the correlation coefficient, accurate to three decimal places  

c) Test the significance of the correlation coefficient with a 0.05 level of significance. Include definition of hypotheses, test statistic, p-value or critical value, decision about Ho, and conclusion.

d)      Find the best estimate for the infant mortality rate for a country with mean daily calorie intake of 2800.

PLEASE SHOW ALL THE WORK AND FOLLOW DIRECTIONS ACCURATE AND MARK EACH PART A), B), C), D)

THANK YOU

Answer 1

x	y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
1523	154	1336798.4400	8427.2400	-106139.160
3495	6	665529.6400	3158.4400	-45847.960
1941	114	544939.2400	2683.2400	-38238.760
2678	24	1.4400	1459.2400	45.840
1610	107	1143188.6400	2007.0400	-47900.160
3443	6	583390.4400	3158.4400	-42925.560
1640	153	1079936.6400	8244.6400	-94359.360
3362	7	466215.8400	3047.0400	-37690.560
3429	44	562200.0400	331.2400	-13646.360
3671	7	983667.2400	3047.0400	-54747.360

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	26792.00	622.00	7365867.60	35563.6	-481449.4
mean	2679.20	62.20	SSxx	SSyy	SSxy

a)

Sample size,   n =   10      
here, x̅ = Σx / n=   2679.200          
ȳ = Σy/n =   62.200          
SSxx =    Σ(x-x̅)² =    7365867.6000      
SSxy=   Σ(x-x̅)(y-ȳ) =   -481449.4      
              
estimated slope , ß1 = SSxy/SSxx =   -481449.4/7365867.6=   -0.0654      
intercept,ß0 = y̅-ß1* x̄ =   62.2- (-0.0654 )*2679.2=   237.3184      
              
Regression line is, Ŷ=   237.318   + (   -0.065   )*x

b) correlation coefficient ,    r = SSxy/√(SSx.SSy) =   -0.941

c)

Ho:   ρ = 0  
Ha:   ρ ╪ 0  
n=   10  
alpha,α =    0.05  
correlation , r=   -0.9407  
t-test statistic = r*√(n-2)/√(1-r²) =        -7.8407
DF=n-2 =   8  
p-value =    0.0001  
Decison:   p value < α , So, Reject Ho  

critical t-value =    2.3060  
decision: reject Ho, because test stat > critical value

There is enough evidence of significant correlation

d) Predicted Y at X=   2800   is          
Ŷ=   237.31844   +   -0.06536   *2800=   54.30

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