THINK4

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Pennsylvania State University *

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407

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Statistics

Date

Apr 3, 2024

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pdf

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2

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THINK 1.1 Interpretation of the Slope (4.85): The slope coefficient of 4.85 indicates that for each additional inch in height, the weight of an individual is expected to increase by 4.85 pounds, holding all else constant. This positive slope suggests a direct relationship between height and weight. Interpretation of the Intercept (−154.41): The intercept coefficient of -154.41 pounds can be interpreted as the expected weight of an individual who is zero inches tall. While this interpretation is not meaningful in a practical real-world context (since there are no individuals with zero height), the intercept helps in establishing the baseline level of the regression line within the context of the data set 1.2 The 90% confidence interval for the intercept term (β₀) is approximately (−164.33,−144.49). For a 90% confidence interval, the Z-value (or t-value for large samples) corresponding to the tails of the standard normal distribution (5% in each tail) is approximately 1.645. 1.3 a) The R² for the regression remains 0.1401. b) Intercept (β₀): -70.19 kg Slope (β₁): 2.20 kg per inch T statistic : 5.00 1.4 The R2 remains at 0.1401 1.5 It would stay the same at 0.1401 Intercept (β₀): Approximately -70.04 kilograms Slope (β₁): Approximately 4.21 kilograms per centimeter 2.1 Best Linear Unbiased Estimator.
2.2 Linearity in Parameters, Random Sampling, No Perfect Multicollinearity, Zero Conditional Mean of the Error Terms, Zero Conditional Mean of the Error Terms, No Autocorrelation. 3 a) Increase Sample Size (n). Higher Variance of the Independent Variable (X). Spread out Distribution of the Independent Variable around its Mean. Reducing the Variance of the Error Term (ε). Centering the Independent Variable. Ensuring No Multicollinearity in the Model. b) Increase Sample Size (n). Higher Variance of the Independent Variable (X). Spread out Distribution of the Independent Variable around its Mean. Reducing the Variance of the Error Term (ε). Centering the Independent Variable. Ensuring No Multicollinearity in the Model. c) The distribution of is approximately normal. The mean of this distribution is the true value of the slope coefficient (β₁). The standard deviation (or standard error) of this distribution can be estimated from the data. d) The distribution of is approximately normal. The mean of this distribution is the true value of the intercept (β₀). The standard deviation (or standard error) of this distribution can be estimated from the data.
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