5. Biologists have discovered a new species of fish that gradually increases in weight during the...

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5. Biologists have discovered a new species of fish that gradually increases in weight during the initial period after birth. Researchers hypothesize that this growth is linear. Below is a small study involving 15 fish to investigate the relationship between day after birth and current weight. # Day after birth Weight (grams) 1 35 1900 2 36 2000 3 30 1400 4 40 2800 5 36 3100 67 42 3100 40 3200 8 37 2700 9 41 3300 10 38 2900 11 38 3500 12 41 3700 13 40 3700 14 40 3300 15 41 3300 5.1 When describing correlation, we can choose different correlation coefficients under different situations. Please briefly describe these coefficients and when we should choose them. 5.2 In this question, choose the correlation coefficient you think is appropriate and calculate it. 5.3 Researchers want to know whether there is a relationship between the day of birth and weight, that is, whether day of birth in this kind of fish can be used to predict the weight. Use linear regression model to explore this relationship. What are H0 and H1? 5.4 Use linear regression model to analysis data and provide results and conclusion. Your results should include Hypothesis test scores, results, and corresponding conclusions. 5.5 Draw the linear regression line in a plot. You can do it using any software or by hand, not limited to R 5.6 Are there any outliers in the plot? What is the outliner and what risks does it bring? 5. Biologists have discovered a new species of fish that gradually increases in weight during the initial period after birth. Researchers hypothesize that this growth is linear. Below is a small study involving 15 fish to investigate the relationship between day after birth and current weight. # Day after birth Weight (grams) 1 35 1900 2 36 2000 3 30 1400 4 40 2800 5 36 3100 67 42 3100 40 3200 8 37 2700 9 41 3300 10 38 2900 11 38 3500 12 41 3700 13 40 3700 14 40 3300 15 41 3300 5.1 When describing correlation, we can choose different correlation coefficients under different situations. Please briefly describe these coefficients and when we should choose them. 5.2 In this question, choose the correlation coefficient you think is appropriate and calculate it. 5.3 Researchers want to know whether there is a relationship between the day of birth and weight, that is, whether day of birth in this kind of fish can be used to predict the weight. Use linear regression model to explore this relationship. What are H0 and H1? 5.4 Use linear regression model to analysis data and provide results and conclusion. Your results should include Hypothesis test scores, results, and corresponding conclusions. 5.5 Draw the linear regression line in a plot. You can do it using any software or by hand, not limited to R 5.6 Are there any outliers in the plot? What is the outliner and what risks does it bring?