A). What is the primary difference between a simple linear regression model and

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A). What is the primary difference between a simple linear regression model and a multiple linear regression model? B). Consider the Microsoft Excel output in Figure 1 for a dataset where a multiple linear regression model of the form shown in Equation (1) is being fitted: SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square 0.767506944 Standard Error Observations 0.923065476 0.852049873 11.78657744 ANOVA df MS ance F 5600.452812 1400.113203 10.07831024 0.004960483 7 972.4638544 138.9234078 Total P-value Lower 95% Upper 95% Lower 950% Upper950% 123.1312463 157.2560575 -0.782998431 0.459293792 494.9827336 248.7202 494 9827336 248.7202411 0.757289089 0.279089778 2.713424669 0.030049846 0.097346631 1.417232 0.097346631 1.417231546 X1 2 3 7.518783955 4.010121419 1.874951696 0.10292646 -1.963646404 17.00121 1.963846404 17.00121431 2.483078555 1.809385602 1.372332438 0.212315529 1.795438521 6.761596 -1.795438521 6.761595631 0481135232 055517418 -0.866638343 0.414855921 1.793913562 0.831643 -1.793913562 0.83164309 Figure-1: Excel Output 1).Using Figure-1, what are the least squares estimates of ,A, ,and for the regression model being fitted for this dataset. 2).The third table at the bottom of Figure 1 is used to test the significance of regression for individual regression coefficients using the t-test. Based on P-values appearing in the excel output, which regression coefficients = 0.05 are "significant" in the model and which are not? Make your judgment based on a level of significance of

Explanation / Answer

a) in simple linear regression
we regress y (dependent variable) on only one independent variable
whereas we regresss y on multiple independent variable in multiple regression model

b)
1)
b0^,b1^,..b5^ are coefficients (see last third table, colum coefficients)
b0^ = -123.1312463
b1^ = 0.757589
b2^ = 7.518783
b3^ = 2.483078555
b4^ = -0.481135232

2)
if p-value is less than alpha(0.05)
the variable is significant
here x1 is only significant as its p-value = 0.30004 < 0.05
rest are not significant

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