Question

Hello, I am wondering what should my Ho and Ha be in this case and what should i do to carry out the test and how do i do it Test whether size is an effective predictor of house prices in the regression model. State your null and alternative hypotheses and report the test statistic, decision rule, and conclusion to the test. [2 marks

The regression equation is Y = 392.123X – 320.435

7575 7 2 3 3 05350 977 8 05559 2 8 755-00 2 7.-35 4 2 1 le 3 la 553525231522125522522 5 5 544333331433135533323 72847166812629945214 32211210411011611 1 059995559095625597559 090941970015866994979 596194871922 164 1 01 2345 678901 2 123456789 5-9-0 3 90 0099050950009550 7987838199570962512233 7-1-4-1-1-2-3 - 4 3 4 3 2 5 3224 4 3 23 2 2231223122551532555515 2 2 2 2-3-5-3-2 3-5-2-3 3 4 3 1 5 3 5 4 4 5 3 4 4 1439571834519311928217 0 212011 20222122 1 590390009 9050950009550 79 87838199570962512233 7 - 4 - 1 2 3 1 4 3 4 3 2 5 3 2 2 4 4 3 23 2 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 2222222223333333333444

Answer 1

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This is the case you use T-test inside the linear regression analysis. The regression analysis will throw the ANOVA table which conducts a F-test to check the linear regression' dependent variable has statistically significant against the independent variable.

Here' the linear regression:

State Price Size NJ 375 SUMMARY OUTPUT NJ 200 0.9 NJ 599 365 Regression Statistics NJ Multiple R 0.665678296 NJ 220 2.1 R Square 0.443127594 NJ Adjusted R Square 250 1.9 0.437971368 NJ 2.2 410 Standard Error 530.388718 NJ 110 429 2.8 Observations NJ 325 NJ 235 1.1 ANOVA NY 145 df Significance F 1.3 MS NY 875 Regression 1 24176053.46 24176053.46 85.9402974 2.12293E-15 NY 300 Residual 108 30381716.76 281312.1922 NY 370 Total 109 54557770.22 NY 268 NY 1399 4.8 Coefficients Standard Error tStat Lower 95% Upper 95% Lower 95.0% Upper 95.0% P-value NY 1125 3.1 Intercept 373.7721854 105.6042239 3.539367761 0.000592923 -583.0980777-164.4462931 583.0980777 -164.4462931 NY 299 Size 412.2936781 44.47421073 9.270398988 2.12293E-15 324.1380769 500.4492793 324.1380769 500.4492793 NY 110 NY 2999 PA Linear regression model with correct notation 282 2.6 PA 135 Y" --373.7722412.2936 Size PA 179 1.8 PA 800

The t-test performed in the linear regression analysis will throw a p-value. Its hypothesis is set like this:

Null Hypothesis : Ho: B_size = 0

Alternate Hypothesis: Ha: B_size != 0

Test statistic = 9.27040

Decision Rule : If p-value is less than .05, then conclude that we reject Null hypothesis and the dependent variable has linear relation with independent variable.

Conclusion: p-value is 2.1299*10^-15, meaning the relation is statistically significant.