Question

**R-STUDIO KNOWLEDGE REQUIRED***

PLEASE ANSWER THE FOLLOWING WITH ****R-STUDIO**** CODING- thank you so much!!

I am specifically look for the solution to part ***(h)**** and *****(i)***** below using R-Studio code:

The data set in question is:

IV. Regression Is there a relationship between the number of stories a building has and its height? Some statisticians compiled data on a set of n = 60 buildings reported in the World Almanac. You will use the data set to decide whether height (in feet) can be predicted from the number of stories. (a) Load the data from buildings.txt. (Note that this is a text file, so use the appropriate instruction. If you are having trouble uploading the data, open it to see its contents and type the data in: one vector for heights and one vector for stories. Ignore the year data.) (b) Draw a scatterplot with stories in the x-axis and height in the y-axis. Describe the trend, strength and (c) Find the linear correlation coefficient between these variables. How does it support the description (d) Obtain the linear model and summary. Write down the regression equation that relates height with (e) Test for significance of the regression at α 0.05. State the null and alternative hypotheses. Can the (f) State the coefficient of determination. What percentage of variation in height is explained by the (g) Draw diagnostic plots (a plot of stories vs. residuals, and a normal probability plot for the residuals) shape of the relationship between stories and height. you gave in (b)? stories. Add the line to the scatterplot. model be used for predictions? Justify your conclusion using the summary in (d) number of stories? Do assumptions appear to be satisfied? Obtain a 95% confidence interval for the true value of the slope. How does the interval support your conclusion in (e)? i) What is the estimated height of a building that is 45 stories high? Write a concluding sentence supported by your results above.

YEAR    Height  Stories
1990    770     54
1980    677     47
1990    428     28
1989    410     38
1966    371     29
1976    504     38
1974    1136    80
1991    695     52
1982    551     45
1986    550     40
1931    568     49
1979    504     33
1988    560     50
1973    512     40
1981    448     31
1983    538     40
1968    410     27
1927    409     31
1969    504     35
1988    777     57
1987    496     31
1960    386     26
1984    530     39
1976    360     25
1920    355     23
1931    1250    102
1989    802     72
1907    741     57
1988    739     54
1990    650     56
1973    592     45
1983    577     42
1971    500     36
1969    469     30
1971    320     22
1988    441     31
1989    845     52
1973    435     29
1987    435     34
1931    375     20
1931    364     33
1924    340     18
1931    375     23
1991    450     30
1973    529     38
1976    412     31
1990    722     62
1983    574     48
1984    498     29
1986    493     40
1986    379     30
1992    579     42
1973    458     36
1988    454     33
1979    952     72
1972    784     57
1930    476     34
1978    453     46
1978    440     30
1977    428     21

Answer 1

Here I attach the R code for the given Regression analysis

data=read.csv(file.choose()) # Save this data in a csv file
data
fit <- lm(data$Height ~ data$Stories)
summary(fit)
confint(fit,'data$Stories',level=0.95)

Coefficients Estimate Std. Error t value Pr(>lt| (Intercept) data$stories 90. 3096 11. 2924 20.9622 4.308 6.44e-05☆☆☆ 0.484423. 310 < 2e-16 signif. codes: 0 ***' 0.001 0.01 0.05 '.' 0.1''1 Residual standard error: 58. 33 on 58 degrees of freedom Multiple R-squared: 0.9036, Adjusted R-squared 0.9019 F-statistic: 543.4 on 1 and 58 DF, p-value: < 2.2e-16

The fitted model is given by

Height= 90.3096 + 11.2924 * Stories

h)

The 95% confidence interval for the slope is given by

confint (fit, datasstories ,level-0.95) 2.5% 97.5% data$Stories 10. 32267 12.26208

i)

The estimated height of building that is 45 stories high is

90.3096+11.2924*45= 598.4676

When the stories is 45 high then the height is increased by 598.4676 feet