Question

1. (40 pts) The music on a digital music player can be stored digitally in several formats. A populr format for a digital music player is known as AlFF, short for Audio Interchange File Format. Another format is known as AAC, short for Advanced Audio Coding. Files on a digital music player can be in either of these formats or both. The 25 songs in this data set use a mixtu of these two formats. Complete all parts below. Use file12.xlsx. re (a) Create a dummy variable using the AAC format as the baseline category (group) to represent the format of the song in the data file and then fit a regression model for how much space (in megabytes, MB) is needed to store a song based on the ength of the song (Time in seconds) at of the song, and the interaction of the format and the length of the song (Time in the form seconds). W (round to three decimal places as needed). rite down the regression model including the estimates of the intercept and all slopes Based on the estimated intercept and slopes, (b) what is the fixed space (in megabytes) needed by songs recorded in the AAC format? (c) do songs recorded in the AIFF format need more or less fixed space (in megabytes) to get started than songs recorded in the AAC format? By how many megabytes? (d) how many megabytes per second do songs recorded in the AAC format take? (e) do songs recorded in the AlFF format need more or less space (in megabytes per second) than songs recorded in the AAC format? By how many megabytes per second? (f) Construct a prediction interval for the amount of disk space (in megabytes) required to store a song that is 250 seconds long using AAC and then AlFF format. The approximate 95% prediction interval for the AAC format is ( The approximate 95% prediction interval for the AIFF format is (

Megabytes_(MB)   Time_(seconds)   Format   Format_Dummy
40.23912   247   AIFF  
30.83418   190   AIFF  
3.80637   236   AAC  
37.58726   219   AIFF  
30.99349   183   AIFF  
36.87189   232   AIFF  
52.24241   302   AIFF  
37.98954   233   AIFF  
12.10549   782   AAC  
50.64212   302   AIFF  
36.4404   217   AIFF  
2.4303   165   AAC  
2.19439   146   AAC  
3.97144   249   AAC  
2.20563   142   AAC  
3.32871   209   AAC  
2.54134   161   AAC  
3.66391   239   AAC  
3.18335   211   AAC  
6.0738   402   AAC  
27.5096   158   AIFF  
37.6632   222   AIFF  
29.01152   169   AIFF  
2.51054   162   AAC  
57.58826   357   AIFF  

Answer 1

SR NO MEGABYTES(Y) TIME (x) FORMAT REGRESSION MODEL po+81x1+е 40.23912 247 AIFF 30.83418 190 AIFF 18.2698+0.01579 x1te y 3 3.80637 236 AAC 37.58726 219 AIFF 30.99349 183 AIFF SUMMARY OUTPUT 36.87189 232 AIFF 52 24241 302 AIFF Regression Statistics Multiple R 37.98954 233 AIFF 010668842 782 AAC 12.10549 R Square 0.01138242 Adjusted R Square 0.03160095 50.64212 302 AIFF Standard Error 36.4404 217 AIFF 9.3576433 Observations 24303 165 AAC 25 13 2.19439 146 AAC 14 3.97144 249 AAG ANOVA 15 2.20563 142 AAC df Significance F 16 3.32871 209 AAC Regression Residual 1 99.2291041 99.2291 0.26481 0.611744692 54134 161 AAC 23 8618.522176 374.718 3.66391 239 AAC 18 Tota 24 8717.75128 19 3.18335 211 AAC Coefficients Standard Emor P-value 20 6.0738 402 AAG tStot Lower 95% Upper 95% Lower 95 056 Upper 95.0% 27.5096 18.2698923 8.467533908 215764 0.04164 0.75346393 35.7863207 0.75346393 35.7863207 158 AIFF Intercept 37.6632 222 AIFF X Variable 1 0.01579152 0.030687166 0.5146 0.61174-0.047689723 0.07927276 -0.04768972 0.07927276 23 29.01152 169 AIFF 24 2.51054 162 AAC 25 57.58826 357 AIFF