The following is a regression ofG DP per state based on Income and Populatio. df
ID: 3315968 • Letter: T
Question
The following is a regression ofG DP per state based on Income and Populatio. df MS Number of ob5 F( 2, 48)=6264.46 Prob E R-squared Adj R-squared= 0.9960 Root MSE 51 Model3.3559e+12 2 1.6179e +12 Residual 1.2857e+10 48267852170 0.0000 0. 9962 Total 3.3688e+12 50 .7375e+10 163 66 GDE Coef. Std Err [95% Conf. Interval] PersonalIncome Population 9056131 1.22103E 0051212 cons737 7003 3220.165 -0.23 0.820-7212.2755736.874 1.063325 .0784387 13.56 0.000 -.0008644 002977-0.29 0.773-.0068501 How would you interpret the coefficients of this regression? Here is a graph of Personal Income, GDP, and Population a. What can you do to correct for what you see in the histograms? How do you interpret these coefficients? b. c. Number of ob P2 Prob E R-squared Adj R-squared Root MSE 51 2069-71 0.0000 0-9885 0.9881 -1 1485 38 dif MS 48) Model 54. 59899 63311939 2 27.2994 95 48 .013189987 Residual Total 55.2321094 50 1.10464219 1ogGDE 95 Conf. Interval] logInc logPop 1.428102 -. 4610194 1.983206 1059694 1077108 435146E 13.48 0. 000 -4.28 0. 000 4.5 0.000 1.215036 1.41167 -.7758 -.244 4525 2.858127 1.108285Explanation / Answer
Hello,
Hope you are keeping.
a) The coefficients are simply the slopes of the regression equation and the graph will be steep.
A linear regression model with two predictor variables can be expressed with the following equation:
Y = B0 + B1*X1 + B2*X2 + e.
Here, B0= -737.7003
B1= 1.0633
B2= -0.000086
e is the residual error.
A significant polynomial term can make the interpretation less intuitive because the effect of changing the predictor varies depending on the value of that predictor. Similarly, a significant interaction term indicates that the effect of the predictor varies depending on the value of a different predictor.
Hence, we can say that the fit is really good when compared to the R sqaured value that we get while calculating the regression.
b) It seems like the data is mostly covering the outliers more and having it in vast volumes, it ain't helping the graph. So we can increase the number of intervals in the X-axis to get a better visualisation idea of the graph.
c) A linear regression model with a log-transformed dependent variable and two predictor variables can be expressed in a different form. Although the data set seems to be fine and the fit is almost accurate, the earlier data set had a better fit that this one.
Hope it helped.
Happy Learning. Cheers!
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