![\"\"](\"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/03\/cfa-level-2-t-table-2.36.png\")
<\/p>\nThe following results are obtained from regressing the price of the US Dollar Index (USDX) on inflation rates and real interest rates.<\/p>\n
$$\\small{\\begin{array}{l|c}\\textbf{Regression Statistics}\\\\ \\hline\\text{Multiple R} & 0.8264\\\\ \\hline\\text{R Square} & 0.6830\\\\ \\hline\\text{Adjusted R Square} & 0.5924\\\\ \\hline\\text{Standard Error} & 5.3537\\\\ \\hline\\text{Observations} & 10\\\\ \\end{array}}$$<\/p>\n
$$\\small{\\begin{array}{l|l|l|l|l}{}& \\textbf{Coefficients} & \\textbf{Standard Error} & \\textbf{t Stat} & \\textbf{P-value}\\\\ \\hline\\text{Intercept} & 81 & 7.9659 & 10.1296 & 0.0000\\\\ \\hline\\text{Inflation rates} & -276 & 233.0748 & -1.1833 & 0.2753\\\\ \\hline\\text{Real interest Rates} & 902 & 279.6949 & 3.2266 & 0.0145\\\\ \\end{array}}$$<\/p>\n
Test the null hypothesis that the inflation rate is equal to 0 against the alternative hypothesis that it is not equal to 0 at the 5% significance level and interpret the results<\/p>\n
We are testing the hypothesis:<\/p>\n
\\(H_{o}:b_1=0\\) vs. \\(H_1:b_1\u22600\\)<\/p>\n
The 5% two-tailed critical t-value with \\(10 – 2 – 1 = 7\\) degrees of freedom is 2.365<\/p>\n
<\/p>\n
The null hypothesis is rejected if the t-statistic is either greater than 2.365 or smaller than \u20132.365 (the critical value).<\/p>\n
$$t=\\frac{\\widehat{b_{j}}-b_{H0}}{S_{\\widehat{b_{j}}}}$$<\/p>\n
$$\\begin{align*}t&=\\frac{-276-0}{233.0748}&\\\\&=-1.18\\end{align*}$$<\/p>\n
The t<\/em>-statistic of -1.18 is between the upper and lower critical t<\/em>-values of \u20132.3646 and 2.3646. We cannot reject the null hypothesis and must conclude that the inflation rate regression coefficient is NOT statistically significantly different from 0 at the 5% significance level.<\/p>\n LOS 2 (d) Interpret the results of hypothesis tests of regression coefficients<\/em><\/p>\n","protected":false},"excerpt":{"rendered":" [vsw id=”8E2AbtAb0a8″ source=”youtube” width=”611″ height=”344″ autoplay=”no”] The following results are obtained from regressing the price of the US Dollar Index (USDX) on inflation rates and real interest rates. $$\\small{\\begin{array}{l|c}\\textbf{Regression Statistics}\\\\ \\hline\\text{Multiple R} & 0.8264\\\\ \\hline\\text{R Square} & 0.6830\\\\ \\hline\\text{Adjusted R…<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[102,229],"tags":[216,241,230],"class_list":["post-11804","post","type-post","status-publish","format-standard","hentry","category-cfa-level-2","category-quantitative-method","tag-cfa-level-2","tag-interpreting-the-results-of-hypothesis-tests-of-regression-coefficients","tag-quantitative-method","blog-post","no-post-thumbnail","animate"],"acf":[],"yoast_head":"\n![\"\"](\"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/03\/cfa-level-two-sided-test-1.181.png\")
<\/em>Reading 2: Multiple Regression<\/p>\n