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In: Statistics and Probability

Estimate a simple linear regression model and present the estimated linear equation. Display the regression summary...

Estimate a simple linear regression model and present the estimated linear equation. Display the regression summary table and interpret the intercept and slope coefficient estimates of the linear model.                                                           

Solutions

Expert Solution

let us consider the data of rents and square foot of house

Rental Square
875 1500
900 1900
900 1200
1090 1500
1175 1900
1250 2900
1400 2000
1400 2100
1500 1600
1600 1700
1700 2000
1800 2600
1900 2500
2000 2700
2000 2200
2200 3000
2300 3300
2500 2300
2600 2500
3000 2500
3200 2700
3500 3000
4000 3300
4500 2200
5000 3000
7000 3500

and we want to predict rent of houses

using excel>data>data analysis >Regression

we have

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.687968
R Square 0.473299
Adjusted R Square 0.451354
Standard Error 1082.42
Observations 26
ANOVA
df SS MS F Significance F
Regression 1 25268253 25268253 21.56668 0.000103
Residual 24 28119209 1171634
Total 25 53387462
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept -1491.42 855.5084 -1.74331 0.094079 -3257.1 274.2654
Square 1.624462 0.349798 4.643994 0.000103 0.902513 2.34641

the regression equation is

Rental = -1491.42 +1.625

Slope : for every one square feet increase in area of house then rent will increase by 1.625$

Intercept : if the house size is 0 square feet thrn the rent will be negative i,e- $1491.42

orchestra answered 1 year ago
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