Question

Suppose you are interested in examining whether intellect is related to income. Specifically,
you hypothesize that the higher an individual’s IQ is, the more money s/he is likely to make. In
other words, this hypothesis suggests that IQ (“IQ”) has a positive effect on income (“Income”).
You have collected the following data from n = 6 respondents (“Income” is measured in
thousands):

Observation. IQ Income
1 120 55
2 145 120
3 98 38
4 104 45
5 167 95
6 112 40

a. With these data, estimate and for a linear regression model (hint: make sure to identify
the dependent and independent variables consistent with the above theory). Write a
sentence or two interpreting these coefficients. Be sure to use the regression aid sheet.

Answer 1

IQ is independent varibale

income is dependent variable

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	746.00	285.00	3525.33	3725.50	1654.00
mean	124.33	47.50	SSxx	SSyy	SSxy

sample size ,   n =   6      
here, x̅ = Σx / n=   124.333          
ȳ = Σy/n =   47.500          
SSxx =    Σ(x-x̅)² =    3525.3333      
SSxy=   Σ(x-x̅)(y-ȳ) =   1654.0      
              
estimated slope , ß1 = SSxy/SSxx =   1654/3525.3333=   0.46918      
intercept,ß0 = y̅-ß1* x̄ =   47.5- (0.4692 )*124.3333=   -10.83415      
              
Regression line is, Ŷ=   -10.834   + (   0.469   )*x

slope: 0.469

if IQ score is increased by 1 unit , income will increase by 0.469 units

......

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