Please help me with my problem set thank you

Assignment Solutions
Q1.
(a)
Ans:
    SUMMARY OUTPUT
     
     
     
     
     
     
     
     
    Regression Statistics
     
     
     
     
     
     
     
     
    Multiple R
    0.804
     
     
     
     
     
     
     
    R Square
    0.647
     
     
     
     
     
     
     
    Adjusted R Square
    0.642
     
     
     
     
     
     
     
    Standard Error
    5508.40
     
     
     
     
     
     
     
    Observations
    506.000
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
    ANOVA
     
     
     
     
     
     
     
     
     
    df
    SS
    MS
    F
    Significance F
     
     
     
    Regression
    7.000
    27714999017.5
    3959285573.9
    130.487
    0.000
     
     
     
    Residual
    498.000
    15110532129.0
    30342434.0
     
     
     
     
     
    Total
    505.000
    42825531146.5
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
    Coefficients
    Standard Error
    t Stat
    P-value
    Lower 95%
    Upper 95%
    Lower 95.0%
    Upper 95.0%
    Intercept
    27433.9
    5447.4
    5.0
    0.0
    16731.3
    38136.6
    16731.3
    38136.6
    crime
    -189.5
    37.0
    -5.1
    0.0
    -262.2
    -116.7
    -262.2
    -116.7
    nox
    -2722.1
    396.6
    -6.9
    0.0
    -3501.3
    -1943.0
    -3501.3
    -1943.0
    rooms
    6392.4
    398.3
    16.0
    0.0
    5609.8
    7175.0
    5609.8
    7175.0
    dist
    -1051.5
    185.9
    -5.7
    0.0
    -1416.8
    -686.2
    -1416.8
    -686.2
    radial
    292.6
    73.3
    4.0
    0.0
    148.5
    436.7
    148.5
    436.7
    proptax
    -132.3
    38.2
    -3.5
    0.0
    -207.3
    -57.3
    -207.3
    -57.3
    stratio
    -1229.9
    139.4
    -8.8
    0.0
    -1503.8
    -955.9
    -1503.8
    -955.9
(a) We did a multiple linear regression of median house prices with all other variables except neighbourhood number as we suppose this is just a number to identify neighbourhood.
As shown in the model output attached above,all the independent variables are statistically significant at 0.05 level as all p values are less than 0.05.Also in the ANOVA table,it shows that the model is significant on overall basis as p value associated with F statistics is less than 0.05.We did not consider the higher order forms of independent variables to exclude the possible multicollinearity & overfitting issue.A simple model is better option always.
Residual analysis & diagnostic test shows model is good fit.
As shown above,final equation is
Median House price =27434 -189.5 x crime-2722.1 x nox +6392.4 x rooms -1051.5 x dist +292.6 x radial -132.3 x proptax -1229.9 x stratio
But standard error is a bit on higher side 5508.4
( b)
(1) if we put the values of independent variables associated with neighbourhood 130,we get predicted median house price as 13567.45 whereas actual price is...