a) Describe the relationship between husbands’ and wives’ ages. It is a positively related linear relationship
b) Describe the relationship between husbands’ and wives’ heights. There is no defined relationship as the points and data are way too scattered, overall one could say it has a positive relationship but it is not strong at all.
c) Which plot shows a stronger correlation? Explain your reasoning. The first plot as there is more of a linear relationship than in the second one.
d) Data on heights were originally collected in centimeters, and then converted to inches. Does this conversion affect the correlation between husbands’ and wives’ heights? No it would not change because for both variables the same unit of measurement was used, so the transformation of one to the other would not be significant
a) Describe the relationship between volume and height of these trees. There is a positive but weak relationship between these two variables
b) Describe the relationship between volume and diameter of these trees. This is a positive and reasonably linear relationship between the two variables, in general it is more strongly correlated.
c) Suppose you have height and diameter measurements for another black cherry tree. Which of these variables would be preferable to use to predict the volume of timber in this tree using a simple linear regression model? Explain your reasoning. We would need to use volume and diameter as there is a stronger connection between those two variables and the results would be more valuable.
a) $5,000 more than women? salarym=salaryw+5000
b) 25% more than women? salarym=salaryw*0.25
c) 15% less than women? salarym=salaryw*(1-0.15)
a) Describe the relationship between number of calories and amount of carbohydrates (in grams) that Starbucks food menu items contain There is a positive but weak relationship between these two variables
b) In this scenario, what are the explanatory and response variables? The explanatory variable is calories and the response variable is carbs
c) Why might we want to fit a regression line to these data? Because it would help estimate the amount of carbs given the amount of calories
d) Do these data meet the conditions required for fitting a least squares line? No because the residuals plot does not demonstrate a linear relationship between the two variables,in addition to this the residuals histogram do not have a normal distribution.
a) Write out the linear model. heartweight=(bodyweight*4.034)-0.357
b) Interpret the intercept. It is the expected heart weight for a cat weighting 0 kg, but it is insignificant.
c) Interpret the slope. How much the weight of the heart increases for one additional unit of body weight (in terms of kilos)
d) Interpret R2. There is a 64.66% variability in the weight of hearts that can be explained by the body weights
e) Calculate the correlation coefficient.
sqrt(0.6466)## [1] 0.8041144a) Describe the relationship between the number of cans of beer and BAC. It appears to be a positively linear relationship between the two variables meaning that a higher amount of cans consumed means a higher BAC.
b) Write the equation of the regression line. Interpret the slope and intercept in context. BAC=(cansofbeer*0.018)-0.0127 The slope means that per can of beer the BAC increases by 0.018 units The intercept means the amount needed to be subtracted from the explanatory variable
c) Do the data provide strong evidence that drinking more cans of beer is associated with an increase in blood alcohol? State the null and alternative hypotheses, report the p-value, and state your conclusion. Ho= A higher consumption in number of cans of beer is not associated with an increase in BAC HA= A higher consumption in number of cans of beer is associated with an increase in BAC Due to fact that p-value is smaller than 0.05 the null hypothesis is rejected; thus, drinking more cans of beer increases BAC
d) The correlation coefficient for number of cans of beer and BAC is 0.89. Calculate R2 and interpret it in context.
0.89^2## [1] 0.7921There is a variability of 79% in BAC that is explained by the number of cans of beer
e) Suppose we visit a bar, ask people how many drinks they have had, and also take their BAC. Do you think the relationship between number of drinks and BAC would be as strong as the relationship found in the Ohio State study? No because the study is not maintaining or controlling other possible factors constant. In addition to this I believe the sample size might not be large enough to arrive to a significant conclusion.
a) What is the predicted head circumference for a baby whose gestational age is 28 weeks?
3.91+0.78*28## [1] 25.75b) The standard error for the coefficient of gestational age is 0.35, which is associated with df = 23. Does the model provide strong evidence that gestational age is significantly associated with head circumference? I need help with this one