**STA130H1F – Fall 2020**

**Week 8 Problem Set**

统计课业代做 Instructions How do I hand in these problems for the 11:59 a.m. ET, November 6th deadline? Your complete .Rmd file that you create for this problem

**Instructions **

**How do I hand in these problems for the 11:59 a.m. ET, November 6th deadline? **

Your complete .Rmd file that you create for this problem set AND the resulting .pdf (i.e., the one you ‘Knit to PDF’ from your .Rmd fifile) must be uploaded into a Quercus assignment (link: https://q.utoronto.ca/courses/184002/assignments/465449?module_item_id=1925503) by 11:59 a.m. ET, on November 6th. Late problem sets or problems submitted another way (e.g., by email) are *not *accepted.

**Problem set grading 统计课业代做**

There are two parts to your problem set. One is largely R-based with short written answers and the other is more focused on writing. We recommend you use a word processing software like Microsoft Word to check for grammar errors in your written work. Note: there can be issues copying from Word to R Markdown so it may be easier to write in this file first and then copy the text to Word. Then you can make any changes flagged in Word directly in this file.

**Part 1 统计课业代做**

**Question 1 **

In a 1965 article, George Moore predicted the number of transistors on processors would double every year. He projected that level of growth would continue for at least another decade. A decade later, in 1975, he revised the forecast to doubling every two years. This is now commonly known as Moore’s law.

The processors.csv dataset contains a sample of data on processors, scraped from Wikipedia about the number of transistors in central processing units (CPUs) and general processing units (GPUs). It also shows the name of the processor and the year it was introduced.

processors <-read_csv("processors.csv")glimpse(processors) ## Rows: 299 ## Columns: 4 ## $ processor <chr> "Intel 4004 (4-bit, 16-pin)", "Intel 8008 (8-bit, ... ## $ year <dbl> 1971, 1972, 1973, 1973, 1974, 1974, 1974, 1974, 19... ## $ transistor_count <dbl> 2250, 3500, 2500, 11000, 3000, 4100, 6000, 8000, 4... ## $ unit_type <chr> "CPU", "CPU", "CPU", "CPU", "CPU", "CPU", "CPU", "...

**(a) Create an appropriate plot for the number of transistors per year, faceted by ****unit_type****. **

**(b) Briefly explain whether you think it is appropriate to fit a straight line through this plot ****as it is displayed? **

**(c) Add a new variable called ****log_transistors ****to the dataset. You can use ****mutate() ****and the ****log() ****function. **

**(d) Plot the association between ****log_transistors ****and ****year****, faceted by ****unit_type ****and use ****geom_smooth(se=FALSE, method=”lm”) ****to add a line of best fit to both plots. Describe this asso****ciation in each plot. **

##### Note: 统计课业代做

You will learn more about transforming variables in future courses and are not required to be able to explain why we’ve done this here. You can just treat log_transistors as we have other variables in class and refer to it as “the log number of transistors”.

**(e) Before calculating anything, do you think the correlation is stronger between log transistor ****count and year for GPUs or CPUs? Justify your answer. **

**(f) Calculate the correlation between ****log_transistors ****and ****year ****for CPUs and GPUs. You may ****find ****group_by()****, ****summarise() ****and ****cor() ****to be helpful functions. **

**(g) Write down a simple linear regression model to predict log number of transistors in a ****processor based on the year it was introduced. Be sure to explain each term in the model. **

##### Hint:

If you copy math equations from another software into your .Rmd document, you’ll get errors when trying to knit. Instead, you should type your math equations directly in your .Rmd document. Here are some tips and examples for doing this:

**(h) State the null and alternative hypotheses you would use assess whether year is a useful ****predictor of the log number of transistors in this linear regression model. **

**(i) Restrict your data to CPUs and use R to fit the linear model that corresponds with your line ****of best fit above. Report the fitted equation of the line. Interpret the regression coefficients ****in the context of this data AND make a conclusion about the hypotheses you defined above. **

**(j) Briefly explain why or why not the interpretation of the intercept is helpful for under****standing Moore’s Law. **

**(k) Get the ***R²* **for your model and write one sentence interpreting it in context. **

**Question 2 统计课业代做**

**(Adapted from Exercise 7.18 in Dietz, Barr, Cetinkaya-Rundel, ****“OpenIntro Statistics”, Second Edition) **

The starbucks.csv dataset contains data on calories and carbohydrates (in grams) in Starbucks food menu items.

starbucksdata<-read_csv("starbucks.csv")glimpse(starbucksdata) ## Rows: 77 ## Columns: 7 ## $ item <chr> "8-Grain Roll", "Apple Bran Muffin", "Apple Fritter", "Ban... ## $ calories <dbl> 350, 350, 420, 490, 130, 370, 460, 370, 310, 420, 380, 320... ## $ fat <dbl> 8, 9, 20, 19, 6, 14, 22, 14, 18, 25, 17, 12, 17, 21, 5, 18... ## $ carb <dbl> 67, 64, 59, 75, 17, 47, 61, 55, 32, 39, 51, 53, 34, 57, 52... ## $ fiber <dbl> 5, 7, 0, 4, 0, 5, 2, 0, 0, 0, 2, 3, 2, 2, 3, 3, 2, 3, 0, 2... ## $ protein <dbl> 10, 6, 5, 7, 0, 6, 7, 6, 5, 7, 4, 6, 5, 5, 12, 7, 8, 6, 0,... ## $ type <chr> "bakery", "bakery", "bakery", "bakery", "bakery", "bakery"...

**(a) Produce a plot that shows the association between carbohydrates and calories in Starbucks ****menu items. Describe this association. **

**(b) Before calculating anything, estimate the correlation coefficient between carbohydrates ****and calorie content in Starbucks menu items based on the plot you produced in (a). Justify ****your answer. **

**(c) Calculate the correlation between carbohydrate and calorie content of Starbucks menu ****items. How does this compare to your estimate in part (b)? **

**(d) Write down a simple linear regression model to predict calories based on carbohydrate ****content of Starbucks menu items. Be sure to explain each term in the model. **

**(e) 统计课业代做**

**State the null and alternative hypotheses you would use assess whether there is a linear ****association between the two variables. **

**(f) Use R to fit the regression model in (d) to these data. Report the fitted regression line. ****Interpret the regression coefficients in the context of this study AND make a conclusion about ****the hypotheses you defined above. **

**(g) Add the estimated linear regression line that you calculated in (d) to the plot you generated ****in (a). Compute the coefficient of determination, ***R²* **. How well does the linear regression line ****seem to capture the relationship between ****carb ****and ****calories****? Justify your answer. **

**(h) Based on the Starbucks data, create a new dataset called ****starbucks_lunch ****which only contains food items which are of one of two types: “sandwich” and ****“bistro box”. Create a boxplot comparing the distribution of calories for these ****two types of items. **

**(g) Fit a linear regression model to test whether there is a difference ****in mean calories for items of type “bistro box” and items of type ****“sandwich”. Write a sentence summarizing your conclusion.**

**Part 2 统计课业代做**

You have just been hired as the first statistician for a start up company. Congratulations! You were hired because the owners are looking to add more credibility to their work by testing if their rubber duckies are significantly better than their competitors. This is based on whether children enjoy their bath time more with their rubber duckie or their major competitor’s (Mr. Quacks). Each child enrolled in the study received either their rubber duckie or one from their major competitor. An adult in the household reported how much enjoyment their children got from playing with the rubber duckie on a scale from 1 to 100.

The big boss (Daisy Duck) has heard about his competitors use linear regression for their own studies and wants you to use the same. However, the big boss does not actually know what linear regression is. Therefore, you need to craft an email explaining to the boss what linear regression is, and whether it would be appropriate to use it for the proposed analysis. You should write out a hypothetical linear regression equation for the experiment and define what each part of the equation is in simple terms. Make sure to use a minimum of 2 vocabulary words and define what they mean for a nonstatistical audience.

*Other things to consider: 统计课业代做*

- Try to not spend more than 20 minutes on the prompt.
- Aim for more than 200 but less than 500 words.
- Use full sentences.
- Grammar is not the main focus of this assessment, but it is important that you communicate in a clear and professional manner (i.e., no slang or emojis should appear).

*Vocabulary *

- Linear relationship
- Approximately linear
- Non-linear
- Correlation
- Slope
- Intercept
- (Simple) linear regression
- Regression model
- Parameter
- Regression coefficients
- Fitted regression line
- Explanatory/independent variable
- Dependent variable
- Measure of model fit
- Coefficient of determination
- Error
- Residual
- Least-squares
- Least-squares estimator

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