lab-starter-code-4-HW2-answers.ipynb

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   "source": [
    "# Lesson 4 Independent Practice"
   ]
  },
  {
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   "metadata": {
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   "source": [
    "# For this exercise, we are going to take a look at several studies and outputs in order to get comfortable reading outputs and practicing hypothesis testing."
   ]
  },
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   "metadata": {},
   "source": [
    "## Data output 1\n",
    "This dataset examines the association between an outcome and generic variables x1, x2, x3\n",
    "<img src='../../assets/images/generic-output.png'>"
   ]
  },
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   "source": [
    "#### Question 1.1 X6 has an association with the outcome of -0.2. Is this finding statistically significant? "
   ]
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   "source": [
    "This finding is not statistically significant as the P-value is 0.21 which is much greater than the acceptable value of 0.05. Also, the t-statistic of -1.29 has an abosolute value which is much less than 2."
   ]
  },
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   "metadata": {},
   "source": [
    "#### Question 1.2 Which of the variables X1, X3, and X6 have a statistically significant finding? "
   ]
  },
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   "source": [
    "X1 has a statitically significant relationship. X3 is marginally statistically significant as the P-value is 0.053. X6 is not statistically significant."
   ]
  },
  {
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   "metadata": {},
   "source": [
    "#### Question 1.3 What does a 95% CI of 0.38-0.866 indicate? "
   ]
  },
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   "source": [
    "Although the coefficient of X1 is estimated to be 0.62, there is a 95% probability that it is between 0.38 and 0.87."
   ]
  },
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   "metadata": {},
   "source": [
    "## Data Output 2 \n",
    "This is a data set of different animals. We measured the brain size and body size of each animale in our data set. We aim to determine if there is an association between the body size and brain size of animals in our dataset."
   ]
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   "source": [
    "<img src=\"../../assets/images/body-size.png\">"
   ]
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   "metadata": {},
   "source": [
    "#### Question 2.1 What is the outcome in this model? "
   ]
  },
  {
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   "source": [
    "The outcome of this analysis is that there is a strong link between body size and brain size. The outcome of the regression are the intercept and the coefficient on the body variable, and the regression statistics (R-squared and F-statistic etc.)."
   ]
  },
  {
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   "metadata": {},
   "source": [
    "#### Question 2.2 What is the predictor in this model? \n"
   ]
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   "source": [
    "Answer: The predictor variable is body size."
   ]
  },
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   "metadata": {},
   "source": [
    "#### Question 2.3 What is the association body and brain size? \n"
   ]
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   "source": [
    "Answer: There is a strong positive association between body size and brain size. The regression coefficient of 0.97 means that there is a close to one-on-one relationship (with appropriate units for body size and brain size)."
   ]
  },
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   "metadata": {},
   "source": [
    "#### Question 2.4 Is this relationship statistically significant? How did you decide?"
   ]
  },
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   "source": [
    "Answer: This relationship is strongly statitically significant as the adjusted R-square of the regression is 0.87 and the p-value of the regression (Prob(F-Statistic)) is virtually 0. The p-value of the predictor variable, body size is almost 0 and is much below the 0.05 threshold for significance."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Question 2.5 Is this relationship biologically significant? What other information would you need to decide this?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Answer: The table only allows us to make statistical inference. We cannot answer the question about biological significance as we do not know why larger animals have a larger brain, and what is the biological significance of brian size and body size."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data Set 3: A study about french fries and diabetes\n",
    "Take a look at the abstract"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"../../assets/images/fry-abstract.png\">"
   ]
  },
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   "source": [
    "### Table 1 - Review Table 1"
   ]
  },
  {
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   "metadata": {},
   "source": [
    "<img src='../../assets/images/fry-table1.png'>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Question 3.1 Is there a statistically significant diffence by age among the different levels of fry or potato intake?"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Answer:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"../../assets/images/fry-table2.png\">"
   ]
  },
  {
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   "metadata": {
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   },
   "source": [
    "#### Question 3.2 What are the numbers in the parentheses?"
   ]
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   "metadata": {},
   "source": [
    "Answer: The numbers in parenthesis are the 95% Confidence Interval upper and lower limits. For example, the regression coefficient for age-adjusted RR for Quintile 5 is 1.13 but there is a 95% chance that it lies between 1.03 and 1.25."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Question 3.3 Is the risk of diabetes statistically significant for women who eat the highest mean servings of potatos (quintile 5) compared to the lowest group (quintile 1)?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "Answer: Yes, for example the multivariate relative risk (RR) for quintile 5 vs. quintile 1 is 1.14 when the results are adjusted for age, and dietary and non-dietary factors. The 95% confidence interval of 1.02 to 1.26 excludes 1, which means that the results are significantly greater than the value for quintile 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Question 3.4 Is the risk of diabetes statistically significant for women who eat the second lowest mean servings of potatos (quintile 2) compared to the lowest group (quintile 1)?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Answer: The multivariate relative risk of 1.05 comparing quintile 2 with quintile 1 has a 95% confidence interval of 0.95 and 1.16 for results adjusted for age, dietary and non-dietary factors. Since the 95% CI includes 1, the risk of diabetes for quintile 2 is not statistically significantly different than that for quintile 1."
   ]
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