Question

8. (20 marks) One end A of an elastic string was attached to a horizontal bar and a mass m grams, was attached to the other end B. The mass was suspended freely and allowed to settle vertically below A. The length AB. Imm, was recorded, for various masses as follows: m100 200 300 400 500 600 228 236 256 278 285 301 Part of the output from fitting the simple linear regression for predicting the length 1 from mass m is shown below: Coefficients: Estimate Std. Error t value Prit) (Intercept) 210.60000 4.06706 51-78 8.32e-07 0.15257 0.0104414.61 0.000128 Signif. codes:0**0.0010.010.05 0.1 1 Residual standard error: 4.369 on 4 degrees of freedom Multiple R-squared: 0.9816, Adjusted R-squared: 0.977 F-statistic: 213.4 on 1 and 4 DF, p-value: 0.0001277 (a) Write down the least squares line of regression of l on m. (b) What is the expected length AB for a mass of 290 grams? (c) Interpret the estimated slope of the fitted model. (d) (2 marks) (2 marks) (2 marks) Is there a significant linear relationship between length I and mass m? Provide a null hypothesis, a test statistic, p-value, and conclusion. How would you comment on whether this model fits the data based on the R results given above? Suppose now you are given more observations and your dataset ElasticString has 200 observations in total. Write down your R code to i. build a linear regression model, and (4 marks) (e) (2 marks) (t) (3 marks) (5 marks) ii. estimate the testing mean squared error.

Answer 1

2 in 10000

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