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Test for the significance of ß, at the 1% level of significance. State the null and alternative hypotheses. (Enter != for as needed.) B3=0 B3!=0 Ho H₂: Find the value of the test statistic. -0.7 x Find the p-value. (Round your answer to four decimal places.) p-value= State your conclusion. O Reject Ho. There is insufficient evidence to conclude that ß, is significant. O Do not reject Ho. There is sufficient evidence to conclude that , is significant. O Reject Ho- There is sufficient evidence to conclude that , is significant. Do not reject Ho. There is insufficient evidence to conclude that B, is significant. (d) What are the degrees of freedom for the sum of squares explained by the regression (SSR)? What are the degrees of freedom for the sum of squares due to error (SSE)? (e) Test whether or not there is a significant relationship between the monthly expenditure on food and the independent variables. Use a 0.01 level of significance. State the null and alternative hypotheses. O Ho: Bo O H₂: Po=0

Test for the significance of ß, at the 1% level of significance. State the null and alternative hypotheses. (Enter != for as needed.) B3=0 B3!=0 Ho H₂: Find the value of the test statistic. -0.7 x Find the p-value. (Round your answer to four decimal places.) p-value= State your conclusion. O Reject Ho. There is insufficient evidence to conclude that ß, is significant. O Do not reject Ho. There is sufficient evidence to conclude that , is significant. O Reject Ho- There is sufficient evidence to conclude that , is significant. Do not reject Ho. There is insufficient evidence to conclude that B, is significant. (d) What are the degrees of freedom for the sum of squares explained by the regression (SSR)? What are the degrees of freedom for the sum of squares due to error (SSE)? (e) Test whether or not there is a significant relationship between the monthly expenditure on food and the independent variables. Use a 0.01 level of significance. State the null and alternative hypotheses. O Ho: Bo O H₂: Po=0

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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esc You may need to use the appropriate technology to answer this question. A sample of 23 families was taken for a study. The objective of the study was to estimate the factors that determine the monthly expenditure (in dollars) on food for families. The independent variables included in the analysis were the number of members in the family (x₁), the number of meals eaten outside (x₂), and a dummy variable (x3) that equals 1 if a family member is on a diet and equals 0 if there is no family member on a diet. The following regression results were obtained. ŷ = Intercept ? X1 X2 ANOVA Ho: X3 Coefficients Regression Residual (Error) f2 474.31 51.94 13.72 -1.12 df (a) Write out the estimated regression equation. Standard Error SS 1,852.50 56.6 3,188.25 1,062.75 圓 ***** 9.8 2.8 16.0 474.31 +51.94x₁ + 13.72x2-1.12x3 (b) Interpret all coefficients. An additional member in the family increases the monthly expenditure in dollars on average by $51.94 monthly expenditure on food in dollars on average by $ 13.72 family member is on a diet. f5 MS (c) Test for the significance of B₁ at the 1% level of significance. State the null and alternative hypotheses. (Enter != for = as needed.) B₁=0 97.50 J f6 4- f7 ♫+ holding all other variables constant. An additional meal eaten outside increases the ✓, holding all other variables constant. The monthly food expenditures in dollars decrease on average by $ 1.12 ✔ if a f8 KAA fg 6 DII f10 DDI f11 f12 insert prt sc delete home end 1:56 PM 12/3/2022 pg up 5 + pg dn
Transcribed Image Text:esc You may need to use the appropriate technology to answer this question. A sample of 23 families was taken for a study. The objective of the study was to estimate the factors that determine the monthly expenditure (in dollars) on food for families. The independent variables included in the analysis were the number of members in the family (x₁), the number of meals eaten outside (x₂), and a dummy variable (x3) that equals 1 if a family member is on a diet and equals 0 if there is no family member on a diet. The following regression results were obtained. ŷ = Intercept ? X1 X2 ANOVA Ho: X3 Coefficients Regression Residual (Error) f2 474.31 51.94 13.72 -1.12 df (a) Write out the estimated regression equation. Standard Error SS 1,852.50 56.6 3,188.25 1,062.75 圓 ***** 9.8 2.8 16.0 474.31 +51.94x₁ + 13.72x2-1.12x3 (b) Interpret all coefficients. An additional member in the family increases the monthly expenditure in dollars on average by $51.94 monthly expenditure on food in dollars on average by $ 13.72 family member is on a diet. f5 MS (c) Test for the significance of B₁ at the 1% level of significance. State the null and alternative hypotheses. (Enter != for = as needed.) B₁=0 97.50 J f6 4- f7 ♫+ holding all other variables constant. An additional meal eaten outside increases the ✓, holding all other variables constant. The monthly food expenditures in dollars decrease on average by $ 1.12 ✔ if a f8 KAA fg 6 DII f10 DDI f11 f12 insert prt sc delete home end 1:56 PM 12/3/2022 pg up 5 + pg dn
esc You may need to use the appropriate technology to answer this question. A sample of 23 families was taken for a study. The objective of the study was to estimate the factors that determine the monthly expenditure (in dollars) on food for families. The independent variables included in the analysis were the number of members in the family (x₁), the number of meals eaten outside (x₂), and a dummy variable (x3) that equals 1 if a family member is on a diet and equals 0 if there is no family member on a diet. The following regression results were obtained. ŷ = Intercept ? X1 X2 ANOVA Ho: X3 Coefficients Regression Residual (Error) f2 474.31 51.94 13.72 -1.12 df (a) Write out the estimated regression equation. Standard Error SS 1,852.50 56.6 3,188.25 1,062.75 圓 ***** 9.8 2.8 16.0 474.31 +51.94x₁ + 13.72x2-1.12x3 (b) Interpret all coefficients. An additional member in the family increases the monthly expenditure in dollars on average by $51.94 monthly expenditure on food in dollars on average by $ 13.72 family member is on a diet. f5 MS (c) Test for the significance of B₁ at the 1% level of significance. State the null and alternative hypotheses. (Enter != for = as needed.) B₁=0 97.50 J f6 4- f7 ♫+ holding all other variables constant. An additional meal eaten outside increases the ✓, holding all other variables constant. The monthly food expenditures in dollars decrease on average by $ 1.12 ✔ if a f8 KAA fg 6 DII f10 DDI f11 f12 insert prt sc delete home end 1:56 PM 12/3/2022 pg up 5 + pg dn
Transcribed Image Text:esc You may need to use the appropriate technology to answer this question. A sample of 23 families was taken for a study. The objective of the study was to estimate the factors that determine the monthly expenditure (in dollars) on food for families. The independent variables included in the analysis were the number of members in the family (x₁), the number of meals eaten outside (x₂), and a dummy variable (x3) that equals 1 if a family member is on a diet and equals 0 if there is no family member on a diet. The following regression results were obtained. ŷ = Intercept ? X1 X2 ANOVA Ho: X3 Coefficients Regression Residual (Error) f2 474.31 51.94 13.72 -1.12 df (a) Write out the estimated regression equation. Standard Error SS 1,852.50 56.6 3,188.25 1,062.75 圓 ***** 9.8 2.8 16.0 474.31 +51.94x₁ + 13.72x2-1.12x3 (b) Interpret all coefficients. An additional member in the family increases the monthly expenditure in dollars on average by $51.94 monthly expenditure on food in dollars on average by $ 13.72 family member is on a diet. f5 MS (c) Test for the significance of B₁ at the 1% level of significance. State the null and alternative hypotheses. (Enter != for = as needed.) B₁=0 97.50 J f6 4- f7 ♫+ holding all other variables constant. An additional meal eaten outside increases the ✓, holding all other variables constant. The monthly food expenditures in dollars decrease on average by $ 1.12 ✔ if a f8 KAA fg 6 DII f10 DDI f11 f12 insert prt sc delete home end 1:56 PM 12/3/2022 pg up 5 + pg dn
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