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Broadband internet and poverty rates-Data from the 2019 American Community Survey records the percent of the population below the poverty level (Poverty) and the percent of households that have a broadband internet subscription (Broadband) for each county in the United States. Grant is a statistics student. For a class project, he selects a random sample of 120 US counties for which this data is recorded and constructs a linear regression model using Poverty as the explanatory variable and Broadband as the response variable. A scatterplot of Grant's data is shown. US County Data 2019 Grant uses statistical software to fit a linear model to the data. A summary of that model fit is given below: Coefficients Estimate Std Error t value Pr(> [t (Intercept) 94.93006 1.47348 64,42596 2e-16 -1.04708 0.09435 -11.09797 2e-16 Poverty Residual standard error: 5.52424 on 118 degrees of freedom Multiple R-squared: 0.51071, Adjusted R-squared: 0.50656 1. Use the computer output to write the estimated linear regression equation for predicting Broadband from Poverty. y= Interpret the slope and intercept of the linear regression model: 2. An increase of 1 point in Poverty is associated with a(n) ? 3. A county with a Poverty value of 0 would have an expected value of ✓ of in Broadband. in Broadband. 10 5 Percent of population below the poverty level

Broadband internet and poverty rates-Data from the 2019 American Community Survey records the percent of the population below the poverty level (Poverty) and the percent of households that have a broadband internet subscription (Broadband) for each county in the United States. Grant is a statistics student. For a class project, he selects a random sample of 120 US counties for which this data is recorded and constructs a linear regression model using Poverty as the explanatory variable and Broadband as the response variable. A scatterplot of Grant's data is shown. US County Data 2019 Grant uses statistical software to fit a linear model to the data. A summary of that model fit is given below: Coefficients Estimate Std Error t value Pr(> [t (Intercept) 94.93006 1.47348 64,42596 2e-16 -1.04708 0.09435 -11.09797 2e-16 Poverty Residual standard error: 5.52424 on 118 degrees of freedom Multiple R-squared: 0.51071, Adjusted R-squared: 0.50656 1. Use the computer output to write the estimated linear regression equation for predicting Broadband from Poverty. y= Interpret the slope and intercept of the linear regression model: 2. An increase of 1 point in Poverty is associated with a(n) ? 3. A county with a Poverty value of 0 would have an expected value of ✓ of in Broadband. in Broadband. 10 5 Percent of population below the poverty level

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.2: The Least Square Line
Problem 8E
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Broadband internet and poverty rates - Data from the 2019 American Community Survey records the percent of the population below the poverty level (Poverty) and the percent of households that have a broadband internet subscription (Broadband) for each county in the United States. Grant is a statistics student. For a class project, he selects a random sample of 120 US counties for which this data is recorded and constructs a linear regression model using Poverty as the explanatory variable and Broadband as the response variable. A scatterplot of Grant's data is shown. US County Data 2019 Grant uses statistical software to fit a linear model to the data. A summary of that model fit is given below: Coefficients Estimate Std Error t value Pr(> [r) (Intercept) 94.93006 1.47348 64.42596 2e-16 2e-16 -1.04708 0.09435 -11.09797 Poverty Residual standard error: 5.52424 on 118 degrees of freedom Multiple R-squared: 0.51071, Adjusted R-squared: 0.50656 1. Use the computer output to write the estimated linear regression equation for predicting Broadband from Poverty. y= Interpret the slope and intercept of the linear regression model: 2. An increase of 1 point in Poverty is associated with a(n) ? + 3. A county with a Poverty value of 0 would have an expected value of OC. Ho B₁b₁ vs. H₁ B₁ b₁ : 4. Which of the following is the correlation coefficient for the linear relationship between Poverty and Broadband? OA. -0.7146 OB. 0.5107 OC. -0.5066 OD. 0.7146 OD. Ho B₁0 vs. H: ₁0 = 6. Based on the computer output, what is the test statistic for the test in part 5? Test statistic: 5. What are the null and alternative hypotheses to test if there is a linear relationship between Poverty and Broadband? OA. Ho: b₁ = 0 vs. H₁: b₁ #0 OB. Ho: ₁0 vs. H₁ : ₁ > 0 of Estimated value= in Broadband. in Broadband. 7. Based on the computer output, the results of the hypothesis test tell us that we have ? Residual = evidence that there? 8. In Illinois, Peoria County has a Poverty value of 15.6. Calculate the estimated value for this county's Broadband value that is predicted by the linear model. 9. Peoria County's actual Broadband value was 78. Use this information and your result from part 8 to calculate the residual for this county. 9 8 5 20 25 30 Percent of population below the poverty level V a linear relationship between Poverty and Broadband. 10 15
Transcribed Image Text:Broadband internet and poverty rates - Data from the 2019 American Community Survey records the percent of the population below the poverty level (Poverty) and the percent of households that have a broadband internet subscription (Broadband) for each county in the United States. Grant is a statistics student. For a class project, he selects a random sample of 120 US counties for which this data is recorded and constructs a linear regression model using Poverty as the explanatory variable and Broadband as the response variable. A scatterplot of Grant's data is shown. US County Data 2019 Grant uses statistical software to fit a linear model to the data. A summary of that model fit is given below: Coefficients Estimate Std Error t value Pr(> [r) (Intercept) 94.93006 1.47348 64.42596 2e-16 2e-16 -1.04708 0.09435 -11.09797 Poverty Residual standard error: 5.52424 on 118 degrees of freedom Multiple R-squared: 0.51071, Adjusted R-squared: 0.50656 1. Use the computer output to write the estimated linear regression equation for predicting Broadband from Poverty. y= Interpret the slope and intercept of the linear regression model: 2. An increase of 1 point in Poverty is associated with a(n) ? + 3. A county with a Poverty value of 0 would have an expected value of OC. Ho B₁b₁ vs. H₁ B₁ b₁ : 4. Which of the following is the correlation coefficient for the linear relationship between Poverty and Broadband? OA. -0.7146 OB. 0.5107 OC. -0.5066 OD. 0.7146 OD. Ho B₁0 vs. H: ₁0 = 6. Based on the computer output, what is the test statistic for the test in part 5? Test statistic: 5. What are the null and alternative hypotheses to test if there is a linear relationship between Poverty and Broadband? OA. Ho: b₁ = 0 vs. H₁: b₁ #0 OB. Ho: ₁0 vs. H₁ : ₁ > 0 of Estimated value= in Broadband. in Broadband. 7. Based on the computer output, the results of the hypothesis test tell us that we have ? Residual = evidence that there? 8. In Illinois, Peoria County has a Poverty value of 15.6. Calculate the estimated value for this county's Broadband value that is predicted by the linear model. 9. Peoria County's actual Broadband value was 78. Use this information and your result from part 8 to calculate the residual for this county. 9 8 5 20 25 30 Percent of population below the poverty level V a linear relationship between Poverty and Broadband. 10 15
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6. Based on the computer output, what is the test statistic for the test in part 5? Test statistic: 7. Based on the computer output, the results of the hypothesis test tell us that we have ? evidence that there? 8. In Illinois, Peoria County has a Poverty value of 15.6. Calculate the estimated value for this county's Broadband value that is predicted by the linear model. Estimated value= 9. Peoria County's actual Broadband value was 78. Use this information and your result from part 8 to calculate the residual for this county. Residual a linear relationship between Poverty and Broadband.
Transcribed Image Text:6. Based on the computer output, what is the test statistic for the test in part 5? Test statistic: 7. Based on the computer output, the results of the hypothesis test tell us that we have ? evidence that there? 8. In Illinois, Peoria County has a Poverty value of 15.6. Calculate the estimated value for this county's Broadband value that is predicted by the linear model. Estimated value= 9. Peoria County's actual Broadband value was 78. Use this information and your result from part 8 to calculate the residual for this county. Residual a linear relationship between Poverty and Broadband.
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